+
+
+
+
+
+
+
Link to the source code for this example:
+
Open vector_fe_ex6 in new tab.
+
+
The console output of the program:
+
+***************************************************************
+* Running Example vector_fe_ex6:
+* ./example-opt dim=2 element_type=TRI6
+***************************************************************
+
+ Mesh Information:
+ elem_dimensions()={2}
+ spatial_dimension()=2
+ n_nodes()=961
+ n_local_nodes()=961
+ n_elem()=450
+ n_local_elem()=450
+ n_active_elem()=450
+ n_subdomains()=1
+ n_elemsets()=0
+ n_partitions()=1
+ n_processors()=1
+ n_threads()=1
+ processor_id()=0
+ is_prepared()=true
+ is_replicated()=true
+
+ EquationSystems
+ n_systems()=1
+ System #0, "DivGrad"
+ Type "LinearImplicit"
+ Variables="u" "p" "l"
+ Finite Element Types="RAVIART_THOMAS" "MONOMIAL" "SCALAR"
+ Approximation Orders="FIRST" "CONSTANT" "FIRST"
+ n_dofs()=1156
+ n_local_dofs()=1156
+ max(n_local_dofs())=1156
+ n_constrained_dofs()=0
+ n_local_constrained_dofs()=0
+ max(local unconstrained dofs)=1156
+ n_vectors()=1
+ n_matrices()=1
+ DofMap Sparsity
+ Average On-Processor Bandwidth <= 7.66955
+ Average Off-Processor Bandwidth <= 0
+ Maximum On-Processor Bandwidth <= 1156
+ Maximum Off-Processor Bandwidth <= 0
+ DofMap Constraints
+ Number of DoF Constraints = 0
+
+WARNING: Shape function gradients for HDiv elements are not currently being computed!./include/libmesh/hdiv_fe_transformation.h, line 88, compiled Sep 11 2023 at 16:24:29 ***
+WARNING: Shape function curls for HDiv elements are not currently being computed!./include/libmesh/hdiv_fe_transformation.h, line 121, compiled Sep 11 2023 at 16:24:29 ***
+L2 error is: 0.13433
+HDiv semi-norm error is: 0.344125
+HDiv error is: 0.369414
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+* ./example-opt dim=2 element_type=TRI6
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+* ./example-opt dim=2 element_type=TRI7
+***************************************************************
+
+ Mesh Information:
+ elem_dimensions()={2}
+ spatial_dimension()=2
+ n_nodes()=1411
+ n_local_nodes()=1411
+ n_elem()=450
+ n_local_elem()=450
+ n_active_elem()=450
+ n_subdomains()=1
+ n_elemsets()=0
+ n_partitions()=1
+ n_processors()=1
+ n_threads()=1
+ processor_id()=0
+ is_prepared()=true
+ is_replicated()=true
+
+ EquationSystems
+ n_systems()=1
+ System #0, "DivGrad"
+ Type "LinearImplicit"
+ Variables="u" "p" "l"
+ Finite Element Types="RAVIART_THOMAS" "MONOMIAL" "SCALAR"
+ Approximation Orders="FIRST" "CONSTANT" "FIRST"
+ n_dofs()=1156
+ n_local_dofs()=1156
+ max(n_local_dofs())=1156
+ n_constrained_dofs()=0
+ n_local_constrained_dofs()=0
+ max(local unconstrained dofs)=1156
+ n_vectors()=1
+ n_matrices()=1
+ DofMap Sparsity
+ Average On-Processor Bandwidth <= 7.66955
+ Average Off-Processor Bandwidth <= 0
+ Maximum On-Processor Bandwidth <= 1156
+ Maximum Off-Processor Bandwidth <= 0
+ DofMap Constraints
+ Number of DoF Constraints = 0
+
+WARNING: Shape function gradients for HDiv elements are not currently being computed!./include/libmesh/hdiv_fe_transformation.h, line 88, compiled Sep 11 2023 at 16:24:29 ***
+WARNING: Shape function curls for HDiv elements are not currently being computed!./include/libmesh/hdiv_fe_transformation.h, line 121, compiled Sep 11 2023 at 16:24:29 ***
+L2 error is: 0.13433
+HDiv semi-norm error is: 0.344125
+HDiv error is: 0.369414
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+* ./example-opt dim=2 element_type=TRI7
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+* ./example-opt dim=2 element_type=QUAD8
+***************************************************************
+
+ Mesh Information:
+ elem_dimensions()={2}
+ spatial_dimension()=2
+ n_nodes()=736
+ n_local_nodes()=736
+ n_elem()=225
+ n_local_elem()=225
+ n_active_elem()=225
+ n_subdomains()=1
+ n_elemsets()=0
+ n_partitions()=1
+ n_processors()=1
+ n_threads()=1
+ processor_id()=0
+ is_prepared()=true
+ is_replicated()=true
+
+ EquationSystems
+ n_systems()=1
+ System #0, "DivGrad"
+ Type "LinearImplicit"
+ Variables="u" "p" "l"
+ Finite Element Types="RAVIART_THOMAS" "MONOMIAL" "SCALAR"
+ Approximation Orders="FIRST" "CONSTANT" "FIRST"
+ n_dofs()=706
+ n_local_dofs()=706
+ max(n_local_dofs())=706
+ n_constrained_dofs()=0
+ n_local_constrained_dofs()=0
+ max(local unconstrained dofs)=706
+ n_vectors()=1
+ n_matrices()=1
+ DofMap Sparsity
+ Average On-Processor Bandwidth <= 9.3711
+ Average Off-Processor Bandwidth <= 0
+ Maximum On-Processor Bandwidth <= 706
+ Maximum Off-Processor Bandwidth <= 0
+ DofMap Constraints
+ Number of DoF Constraints = 0
+
+WARNING: Shape function gradients for HDiv elements are not currently being computed!./include/libmesh/hdiv_fe_transformation.h, line 88, compiled Sep 11 2023 at 16:24:29 ***
+WARNING: Shape function curls for HDiv elements are not currently being computed!./include/libmesh/hdiv_fe_transformation.h, line 121, compiled Sep 11 2023 at 16:24:29 ***
+L2 error is: 0.13447
+HDiv semi-norm error is: 0.4213
+HDiv error is: 0.44224
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+* ./example-opt dim=2 element_type=QUAD8
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+* ./example-opt dim=2 element_type=QUAD9
+***************************************************************
+
+ Mesh Information:
+ elem_dimensions()={2}
+ spatial_dimension()=2
+ n_nodes()=961
+ n_local_nodes()=961
+ n_elem()=225
+ n_local_elem()=225
+ n_active_elem()=225
+ n_subdomains()=1
+ n_elemsets()=0
+ n_partitions()=1
+ n_processors()=1
+ n_threads()=1
+ processor_id()=0
+ is_prepared()=true
+ is_replicated()=true
+
+ EquationSystems
+ n_systems()=1
+ System #0, "DivGrad"
+ Type "LinearImplicit"
+ Variables="u" "p" "l"
+ Finite Element Types="RAVIART_THOMAS" "MONOMIAL" "SCALAR"
+ Approximation Orders="FIRST" "CONSTANT" "FIRST"
+ n_dofs()=706
+ n_local_dofs()=706
+ max(n_local_dofs())=706
+ n_constrained_dofs()=0
+ n_local_constrained_dofs()=0
+ max(local unconstrained dofs)=706
+ n_vectors()=1
+ n_matrices()=1
+ DofMap Sparsity
+ Average On-Processor Bandwidth <= 9.3711
+ Average Off-Processor Bandwidth <= 0
+ Maximum On-Processor Bandwidth <= 706
+ Maximum Off-Processor Bandwidth <= 0
+ DofMap Constraints
+ Number of DoF Constraints = 0
+
+WARNING: Shape function gradients for HDiv elements are not currently being computed!./include/libmesh/hdiv_fe_transformation.h, line 88, compiled Sep 11 2023 at 16:24:29 ***
+WARNING: Shape function curls for HDiv elements are not currently being computed!./include/libmesh/hdiv_fe_transformation.h, line 121, compiled Sep 11 2023 at 16:24:29 ***
+L2 error is: 0.13447
+HDiv semi-norm error is: 0.4213
+HDiv error is: 0.44224
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+* ./example-opt dim=2 element_type=QUAD9
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+* ./example-opt dim=3 element_type=TET14 grid_size=6
+***************************************************************
+
+ Mesh Information:
+ elem_dimensions()={3}
+ spatial_dimension()=3
+ n_nodes()=19045
+ n_local_nodes()=19045
+ n_elem()=5184
+ n_local_elem()=5184
+ n_active_elem()=5184
+ n_subdomains()=1
+ n_elemsets()=0
+ n_partitions()=1
+ n_processors()=1
+ n_threads()=1
+ processor_id()=0
+ is_prepared()=true
+ is_replicated()=true
+
+ EquationSystems
+ n_systems()=1
+ System #0, "DivGrad"
+ Type "LinearImplicit"
+ Variables="u" "p" "l"
+ Finite Element Types="RAVIART_THOMAS" "MONOMIAL" "SCALAR"
+ Approximation Orders="FIRST" "CONSTANT" "FIRST"
+ n_dofs()=15985
+ n_local_dofs()=15985
+ max(n_local_dofs())=15985
+ n_constrained_dofs()=0
+ n_local_constrained_dofs()=0
+ max(local unconstrained dofs)=15985
+ n_vectors()=1
+ n_matrices()=1
+ DofMap Sparsity
+ Average On-Processor Bandwidth <= 9.48596
+ Average Off-Processor Bandwidth <= 0
+ Maximum On-Processor Bandwidth <= 15985
+ Maximum Off-Processor Bandwidth <= 0
+ DofMap Constraints
+ Number of DoF Constraints = 0
+
+WARNING: Shape function gradients for HDiv elements are not currently being computed!./include/libmesh/hdiv_fe_transformation.h, line 88, compiled Sep 11 2023 at 16:24:29 ***
+WARNING: Shape function curls for HDiv elements are not currently being computed!./include/libmesh/hdiv_fe_transformation.h, line 121, compiled Sep 11 2023 at 16:24:29 ***
+L2 error is: 0.334676
+HDiv semi-norm error is: 0.83716
+HDiv error is: 0.90158
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+* ./example-opt dim=3 element_type=TET14 grid_size=6
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+* ./example-opt dim=3 element_type=HEX27
+***************************************************************
+
+ Mesh Information:
+ elem_dimensions()={3}
+ spatial_dimension()=3
+ n_nodes()=29791
+ n_local_nodes()=29791
+ n_elem()=3375
+ n_local_elem()=3375
+ n_active_elem()=3375
+ n_subdomains()=1
+ n_elemsets()=0
+ n_partitions()=1
+ n_processors()=1
+ n_threads()=1
+ processor_id()=0
+ is_prepared()=true
+ is_replicated()=true
+
+ EquationSystems
+ n_systems()=1
+ System #0, "DivGrad"
+ Type "LinearImplicit"
+ Variables="u" "p" "l"
+ Finite Element Types="RAVIART_THOMAS" "MONOMIAL" "SCALAR"
+ Approximation Orders="FIRST" "CONSTANT" "FIRST"
+ n_dofs()=14176
+ n_local_dofs()=14176
+ max(n_local_dofs())=14176
+ n_constrained_dofs()=0
+ n_local_constrained_dofs()=0
+ max(local unconstrained dofs)=14176
+ n_vectors()=1
+ n_matrices()=1
+ DofMap Sparsity
+ Average On-Processor Bandwidth <= 12.9992
+ Average Off-Processor Bandwidth <= 0
+ Maximum On-Processor Bandwidth <= 14176
+ Maximum Off-Processor Bandwidth <= 0
+ DofMap Constraints
+ Number of DoF Constraints = 0
+
+WARNING: Shape function gradients for HDiv elements are not currently being computed!./include/libmesh/hdiv_fe_transformation.h, line 88, compiled Sep 11 2023 at 16:24:29 ***
+WARNING: Shape function curls for HDiv elements are not currently being computed!./include/libmesh/hdiv_fe_transformation.h, line 121, compiled Sep 11 2023 at 16:24:29 ***
+L2 error is: 0.232486
+HDiv semi-norm error is: 0.773271
+HDiv error is: 0.807464
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+* ./example-opt dim=3 element_type=HEX27
+***************************************************************
+
+
+
+
+
+
+
+
+
+
+
diff --git a/doc/html/src/examples.html b/doc/html/src/examples.html
index 81e66a145e0..0166bdd2367 100644
--- a/doc/html/src/examples.html
+++ b/doc/html/src/examples.html
@@ -156,6 +156,8 @@
A Series of Example Programs
Discontinuous Galerkin Vector Poisson Problem
+
Raviart-Thomas Elements for H(div) Problems in 2D and 3D
+
diff --git a/examples/Makefile.am b/examples/Makefile.am
index fa65259072a..908b0168abe 100644
--- a/examples/Makefile.am
+++ b/examples/Makefile.am
@@ -66,8 +66,9 @@ SUBDIRS = \
vector_fe/vector_fe_ex1 \
vector_fe/vector_fe_ex2 \
vector_fe/vector_fe_ex3 \
- vector_fe/vector_fe_ex4 \
- vector_fe/vector_fe_ex5
+ vector_fe/vector_fe_ex4 \
+ vector_fe/vector_fe_ex5 \
+ vector_fe/vector_fe_ex6
AUTOMAKE_OPTIONS = subdir-objects
diff --git a/examples/Makefile.in b/examples/Makefile.in
index 02af72b97f2..cafa362e042 100644
--- a/examples/Makefile.in
+++ b/examples/Makefile.in
@@ -647,8 +647,9 @@ SUBDIRS = \
vector_fe/vector_fe_ex1 \
vector_fe/vector_fe_ex2 \
vector_fe/vector_fe_ex3 \
- vector_fe/vector_fe_ex4 \
- vector_fe/vector_fe_ex5
+ vector_fe/vector_fe_ex4 \
+ vector_fe/vector_fe_ex5 \
+ vector_fe/vector_fe_ex6
AUTOMAKE_OPTIONS = subdir-objects
AM_CPPFLAGS = $(libmesh_CPPFLAGS) $(libmesh_optional_INCLUDES) \
diff --git a/examples/vector_fe/vector_fe_ex6/Makefile.am b/examples/vector_fe/vector_fe_ex6/Makefile.am
new file mode 100644
index 00000000000..4e575eba307
--- /dev/null
+++ b/examples/vector_fe/vector_fe_ex6/Makefile.am
@@ -0,0 +1,21 @@
+example_name = vector_fe_ex6
+check_SCRIPTS = run.sh
+install_dir = $(examples_install_path)/vector_fe/ex6
+data = div_grad_exact_solution.h solution_function.h vector_fe_ex6.C vector_fe_ex6.in run.sh
+sources = $(data)
+
+CLEANFILES = out.e
+
+# also need to link files for VPATH builds
+if LIBMESH_VPATH_BUILD
+ BUILT_SOURCES = .linkstamp
+.linkstamp:
+ -rm -f vector_fe_ex6.in && $(LN_S) -f $(srcdir)/vector_fe_ex6.in .
+ $(AM_V_GEN)touch .linkstamp
+
+ CLEANFILES += vector_fe_ex6.in .linkstamp
+endif
+
+##############################################
+# include common example environment
+include $(top_srcdir)/examples/Make.common
diff --git a/examples/vector_fe/vector_fe_ex6/Makefile.in b/examples/vector_fe/vector_fe_ex6/Makefile.in
new file mode 100644
index 00000000000..7646efea07b
--- /dev/null
+++ b/examples/vector_fe/vector_fe_ex6/Makefile.in
@@ -0,0 +1,1314 @@
+# Makefile.in generated by automake 1.16.1 from Makefile.am.
+# @configure_input@
+
+# Copyright (C) 1994-2018 Free Software Foundation, Inc.
+
+# This Makefile.in is free software; the Free Software Foundation
+# gives unlimited permission to copy and/or distribute it,
+# with or without modifications, as long as this notice is preserved.
+
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY, to the extent permitted by law; without
+# even the implied warranty of MERCHANTABILITY or FITNESS FOR A
+# PARTICULAR PURPOSE.
+
+@SET_MAKE@
+
+VPATH = @srcdir@
+am__is_gnu_make = { \
+ if test -z '$(MAKELEVEL)'; then \
+ false; \
+ elif test -n '$(MAKE_HOST)'; then \
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+ true; \
+ else \
+ false; \
+ fi; \
+}
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+ ?) ;; \
+ *) echo "am__make_running_with_option: internal error: invalid" \
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+ *\\[\ \ ]*) \
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+ | sed "s/$$bs$$bs[$$bs $$bs ]*//g"`;; \
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+ skip_next=no; \
+ strip_trailopt () \
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+ -*l?*) strip_trailopt 'l';; \
+ -[dEDm]) skip_next=yes;; \
+ -[JT]) skip_next=yes;; \
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+ case $$flg in \
+ *$$target_option*) has_opt=yes; break;; \
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+ test $$has_opt = yes
+am__make_dryrun = (target_option=n; $(am__make_running_with_option))
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+pkgdatadir = $(datadir)/@PACKAGE@
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+am__cd = CDPATH="$${ZSH_VERSION+.}$(PATH_SEPARATOR)" && cd
+install_sh_DATA = $(install_sh) -c -m 644
+install_sh_PROGRAM = $(install_sh) -c
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+INSTALL_HEADER = $(INSTALL_DATA)
+transform = $(program_transform_name)
+NORMAL_INSTALL = :
+PRE_INSTALL = :
+POST_INSTALL = :
+NORMAL_UNINSTALL = :
+PRE_UNINSTALL = :
+POST_UNINSTALL = :
+build_triplet = @build@
+host_triplet = @host@
+target_triplet = @target@
+@LIBMESH_VPATH_BUILD_TRUE@am__append_1 = vector_fe_ex6.in .linkstamp
+check_PROGRAMS = $(am__EXEEXT_1) $(am__EXEEXT_2) $(am__EXEEXT_3) \
+ $(am__EXEEXT_4) $(am__EXEEXT_5)
+@LIBMESH_DBG_MODE_TRUE@am__append_2 = example-dbg
+@LIBMESH_DEVEL_MODE_TRUE@am__append_3 = example-devel
+@LIBMESH_OPT_MODE_TRUE@am__append_4 = example-opt
+@LIBMESH_PROF_MODE_TRUE@am__append_5 = example-prof
+@LIBMESH_OPROF_MODE_TRUE@am__append_6 = example-oprof
+subdir = examples/vector_fe/vector_fe_ex6
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+am__include = @am__include@
+am__leading_dot = @am__leading_dot@
+am__quote = @am__quote@
+am__tar = @am__tar@
+am__untar = @am__untar@
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+build_cpu = @build_cpu@
+build_os = @build_os@
+build_vendor = @build_vendor@
+builddir = @builddir@
+datadir = $(install_dir)
+datarootdir = @datarootdir@
+docdir = @docdir@
+dvidir = @dvidir@
+enabledeprecated = @enabledeprecated@
+enablefwdenums = @enablefwdenums@
+enablelegacyincludepaths = @enablelegacyincludepaths@
+enablepetsc = @enablepetsc@
+enableuniqueptr = @enableuniqueptr@
+enablewarnings = @enablewarnings@
+exec_prefix = @exec_prefix@
+gitquery = @gitquery@
+have_gcov = @have_gcov@
+host = @host@
+host_alias = @host_alias@
+host_cpu = @host_cpu@
+host_os = @host_os@
+host_vendor = @host_vendor@
+htmldir = @htmldir@
+includedir = @includedir@
+infodir = @infodir@
+install_sh = @install_sh@
+libdir = @libdir@
+libexecdir = @libexecdir@
+libmesh_CFLAGS = @libmesh_CFLAGS@
+libmesh_CPPFLAGS = @libmesh_CPPFLAGS@
+libmesh_CXXFLAGS = @libmesh_CXXFLAGS@
+libmesh_LDFLAGS = @libmesh_LDFLAGS@
+libmesh_contrib_INCLUDES = @libmesh_contrib_INCLUDES@
+libmesh_installed_LIBS = @libmesh_installed_LIBS@
+libmesh_optional_INCLUDES = @libmesh_optional_INCLUDES@
+libmesh_optional_LIBS = @libmesh_optional_LIBS@
+libmesh_pkgconfig_requires = @libmesh_pkgconfig_requires@
+libmesh_precision_LIBS = @libmesh_precision_LIBS@
+localedir = @localedir@
+localstatedir = @localstatedir@
+mandir = @mandir@
+mkdir_p = @mkdir_p@
+oldincludedir = @oldincludedir@
+pdfdir = @pdfdir@
+petscmajor = @petscmajor@
+petscmajorminor = @petscmajorminor@
+petscminor = @petscminor@
+petscversion = @petscversion@
+prefix = @prefix@
+program_transform_name = @program_transform_name@
+psdir = @psdir@
+sbindir = @sbindir@
+sharedstatedir = @sharedstatedir@
+srcdir = @srcdir@
+subdirs_extra = @subdirs_extra@
+sysconfdir = @sysconfdir@
+target = @target@
+target_alias = @target_alias@
+target_cpu = @target_cpu@
+target_os = @target_os@
+target_vendor = @target_vendor@
+top_build_prefix = @top_build_prefix@
+top_builddir = @top_builddir@
+top_srcdir = @top_srcdir@
+vtkbuild = @vtkbuild@
+vtkmajor = @vtkmajor@
+vtkversion = @vtkversion@
+example_name = vector_fe_ex6
+check_SCRIPTS = run.sh
+install_dir = $(examples_install_path)/vector_fe/ex6
+data = div_grad_exact_solution.h solution_function.h vector_fe_ex6.C vector_fe_ex6.in run.sh
+sources = $(data)
+
+######################################################################
+#
+# how to make documentation
+#
+CLEANFILES = out.e $(am__append_1) $(example_name).html stdout.log
+
+# also need to link files for VPATH builds
+@LIBMESH_VPATH_BUILD_TRUE@BUILT_SOURCES = .linkstamp
+
+######################################################################
+#
+# Common environment for all examples
+#
+# This file is included by *every* example. If we are careful, common
+# rules like 'make doc' or 'make run' can be defined here, once and
+# for all.
+#
+AUTOMAKE_OPTIONS = subdir-objects
+AM_CPPFLAGS = $(libmesh_optional_INCLUDES) -I$(top_builddir)/include $(libmesh_contrib_INCLUDES)
+AM_CFLAGS = $(libmesh_CFLAGS)
+AM_CXXFLAGS = $(libmesh_CXXFLAGS)
+AM_LDFLAGS = $(libmesh_LDFLAGS)
+examples_source_path = $(top_srcdir)/examples
+examples_install_path = $(prefix)/examples
+data_DATA = $(data) $(top_builddir)/contrib/utils/Makefile
+@LIBMESH_DBG_MODE_TRUE@example_dbg_SOURCES = $(sources)
+@LIBMESH_DBG_MODE_TRUE@example_dbg_CPPFLAGS = $(CPPFLAGS_DBG) $(AM_CPPFLAGS)
+@LIBMESH_DBG_MODE_TRUE@example_dbg_CXXFLAGS = $(CXXFLAGS_DBG)
+@LIBMESH_DBG_MODE_TRUE@example_dbg_LDADD = $(top_builddir)/libmesh_dbg.la
+@LIBMESH_DEVEL_MODE_TRUE@example_devel_SOURCES = $(sources)
+@LIBMESH_DEVEL_MODE_TRUE@example_devel_CPPFLAGS = $(CPPFLAGS_DEVEL) $(AM_CPPFLAGS)
+@LIBMESH_DEVEL_MODE_TRUE@example_devel_CXXFLAGS = $(CXXFLAGS_DEVEL)
+@LIBMESH_DEVEL_MODE_TRUE@example_devel_LDADD = $(top_builddir)/libmesh_devel.la
+@LIBMESH_OPT_MODE_TRUE@example_opt_SOURCES = $(sources)
+@LIBMESH_OPT_MODE_TRUE@example_opt_CPPFLAGS = $(CPPFLAGS_OPT) $(AM_CPPFLAGS)
+@LIBMESH_OPT_MODE_TRUE@example_opt_CXXFLAGS = $(CXXFLAGS_OPT)
+@LIBMESH_OPT_MODE_TRUE@example_opt_LDADD = $(top_builddir)/libmesh_opt.la
+@LIBMESH_PROF_MODE_TRUE@example_prof_SOURCES = $(sources)
+@LIBMESH_PROF_MODE_TRUE@example_prof_CPPFLAGS = $(CPPFLAGS_PROF) $(AM_CPPFLAGS)
+@LIBMESH_PROF_MODE_TRUE@example_prof_CXXFLAGS = $(CXXFLAGS_PROF)
+@LIBMESH_PROF_MODE_TRUE@example_prof_LDADD = $(top_builddir)/libmesh_prof.la
+@LIBMESH_OPROF_MODE_TRUE@example_oprof_SOURCES = $(sources)
+@LIBMESH_OPROF_MODE_TRUE@example_oprof_CPPFLAGS = $(CPPFLAGS_OPROF) $(AM_CPPFLAGS)
+@LIBMESH_OPROF_MODE_TRUE@example_oprof_CXXFLAGS = $(CXXFLAGS_OPROF)
+@LIBMESH_OPROF_MODE_TRUE@example_oprof_LDADD = $(top_builddir)/libmesh_oprof.la
+@LIBMESH_DBG_MODE_TRUE@@LIBMESH_DEVEL_MODE_FALSE@@LIBMESH_OPROF_MODE_FALSE@@LIBMESH_OPT_MODE_FALSE@@LIBMESH_PROF_MODE_FALSE@DOC_PROGRAM = example-dbg
+@LIBMESH_DEVEL_MODE_TRUE@@LIBMESH_OPROF_MODE_FALSE@@LIBMESH_OPT_MODE_FALSE@@LIBMESH_PROF_MODE_FALSE@DOC_PROGRAM = example-devel
+@LIBMESH_OPROF_MODE_FALSE@@LIBMESH_OPT_MODE_FALSE@@LIBMESH_PROF_MODE_TRUE@DOC_PROGRAM = example-prof
+@LIBMESH_OPROF_MODE_TRUE@@LIBMESH_OPT_MODE_FALSE@DOC_PROGRAM = example-oprof
+
+######################################################################
+#
+# Choose a flavor to run when making documentation
+#
+@LIBMESH_OPT_MODE_TRUE@DOC_PROGRAM = example-opt
+@LIBMESH_DBG_MODE_TRUE@@LIBMESH_DEVEL_MODE_FALSE@@LIBMESH_OPROF_MODE_FALSE@@LIBMESH_OPT_MODE_FALSE@@LIBMESH_PROF_MODE_FALSE@DOC_METHOD = dbg
+@LIBMESH_DEVEL_MODE_TRUE@@LIBMESH_OPROF_MODE_FALSE@@LIBMESH_OPT_MODE_FALSE@@LIBMESH_PROF_MODE_FALSE@DOC_METHOD = devel
+@LIBMESH_OPROF_MODE_FALSE@@LIBMESH_OPT_MODE_FALSE@@LIBMESH_PROF_MODE_TRUE@DOC_METHOD = prof
+@LIBMESH_OPROF_MODE_TRUE@@LIBMESH_OPT_MODE_FALSE@DOC_METHOD = oprof
+@LIBMESH_OPT_MODE_TRUE@DOC_METHOD = opt
+
+######################################################################
+#
+# Running the tests
+#
+TESTS_ENVIRONMENT = LIBMESH_DIR=$(abs_top_srcdir); export LIBMESH_DIR; \
+ METHODS="$(METHODS)"; export METHODS; petscmajor=@petscmajor@ \
+ petscminor=@petscminor@
+TESTS = $(check_SCRIPTS)
+all: $(BUILT_SOURCES)
+ $(MAKE) $(AM_MAKEFLAGS) all-am
+
+.SUFFIXES:
+.SUFFIXES: .C .lo .o .obj
+$(srcdir)/Makefile.in: @MAINTAINER_MODE_TRUE@ $(srcdir)/Makefile.am $(top_srcdir)/examples/Make.common $(am__configure_deps)
+ @for dep in $?; do \
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+ && { if test -f $@; then exit 0; else break; fi; }; \
+ exit 1;; \
+ esac; \
+ done; \
+ echo ' cd $(top_srcdir) && $(AUTOMAKE) --gnu examples/vector_fe/vector_fe_ex6/Makefile'; \
+ $(am__cd) $(top_srcdir) && \
+ $(AUTOMAKE) --gnu examples/vector_fe/vector_fe_ex6/Makefile
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+
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+ cd $(top_builddir) && $(MAKE) $(AM_MAKEFLAGS) am--refresh
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+clean-checkPROGRAMS:
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+ echo " rm -f" $$list; \
+ rm -f $$list || exit $$?; \
+ test -n "$(EXEEXT)" || exit 0; \
+ list=`for p in $$list; do echo "$$p"; done | sed 's/$(EXEEXT)$$//'`; \
+ echo " rm -f" $$list; \
+ rm -f $$list
+
+example-dbg$(EXEEXT): $(example_dbg_OBJECTS) $(example_dbg_DEPENDENCIES) $(EXTRA_example_dbg_DEPENDENCIES)
+ @rm -f example-dbg$(EXEEXT)
+ $(AM_V_CXXLD)$(example_dbg_LINK) $(example_dbg_OBJECTS) $(example_dbg_LDADD) $(LIBS)
+
+example-devel$(EXEEXT): $(example_devel_OBJECTS) $(example_devel_DEPENDENCIES) $(EXTRA_example_devel_DEPENDENCIES)
+ @rm -f example-devel$(EXEEXT)
+ $(AM_V_CXXLD)$(example_devel_LINK) $(example_devel_OBJECTS) $(example_devel_LDADD) $(LIBS)
+
+example-oprof$(EXEEXT): $(example_oprof_OBJECTS) $(example_oprof_DEPENDENCIES) $(EXTRA_example_oprof_DEPENDENCIES)
+ @rm -f example-oprof$(EXEEXT)
+ $(AM_V_CXXLD)$(example_oprof_LINK) $(example_oprof_OBJECTS) $(example_oprof_LDADD) $(LIBS)
+
+example-opt$(EXEEXT): $(example_opt_OBJECTS) $(example_opt_DEPENDENCIES) $(EXTRA_example_opt_DEPENDENCIES)
+ @rm -f example-opt$(EXEEXT)
+ $(AM_V_CXXLD)$(example_opt_LINK) $(example_opt_OBJECTS) $(example_opt_LDADD) $(LIBS)
+
+example-prof$(EXEEXT): $(example_prof_OBJECTS) $(example_prof_DEPENDENCIES) $(EXTRA_example_prof_DEPENDENCIES)
+ @rm -f example-prof$(EXEEXT)
+ $(AM_V_CXXLD)$(example_prof_LINK) $(example_prof_OBJECTS) $(example_prof_LDADD) $(LIBS)
+
+mostlyclean-compile:
+ -rm -f *.$(OBJEXT)
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+distclean-compile:
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+am--depfiles: $(am__depfiles_remade)
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+
+example_dbg-vector_fe_ex6.obj: vector_fe_ex6.C
+@am__fastdepCXX_TRUE@ $(AM_V_CXX)$(CXX) $(DEFS) $(DEFAULT_INCLUDES) $(INCLUDES) $(example_dbg_CPPFLAGS) $(CPPFLAGS) $(example_dbg_CXXFLAGS) $(CXXFLAGS) -MT example_dbg-vector_fe_ex6.obj -MD -MP -MF $(DEPDIR)/example_dbg-vector_fe_ex6.Tpo -c -o example_dbg-vector_fe_ex6.obj `if test -f 'vector_fe_ex6.C'; then $(CYGPATH_W) 'vector_fe_ex6.C'; else $(CYGPATH_W) '$(srcdir)/vector_fe_ex6.C'; fi`
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+# include common example environment
+
+# Tell versions [3.59,3.63) of GNU make to not export all variables.
+# Otherwise a system limit (for SysV at least) may be exceeded.
+.NOEXPORT:
diff --git a/examples/vector_fe/vector_fe_ex6/div_grad_exact_solution.h b/examples/vector_fe/vector_fe_ex6/div_grad_exact_solution.h
new file mode 100644
index 00000000000..72a0965e109
--- /dev/null
+++ b/examples/vector_fe/vector_fe_ex6/div_grad_exact_solution.h
@@ -0,0 +1,112 @@
+// The libMesh Finite Element Library.
+// Copyright (C) 2002-2023 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
+
+// This library is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+// Lesser General Public License for more details.
+
+// You should have received a copy of the GNU Lesser General Public
+// License along with this library; if not, write to the Free Software
+// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+
+#ifndef DIV_GRAD_EXACT_SOLUTION_H
+#define DIV_GRAD_EXACT_SOLUTION_H
+
+#include "libmesh/libmesh_common.h"
+#include "libmesh/vector_value.h"
+
+using namespace libMesh;
+
+class DivGradExactSolution
+{
+public:
+ DivGradExactSolution() = default;
+ ~DivGradExactSolution() = default;
+
+ Real scalar(Real x, Real y)
+ {
+ return cos(.5*pi*x)*sin(.5*pi*y);
+ }
+
+ Real scalar(Real x, Real y, Real z)
+ {
+ return cos(.5*pi*x)*sin(.5*pi*y)*cos(.5*pi*z);
+ }
+
+ RealGradient operator() (Real x, Real y)
+ {
+ const Real ux = .5*pi*sin(.5*pi*x)*sin(.5*pi*y);
+ const Real uy = -.5*pi*cos(.5*pi*x)*cos(.5*pi*y);
+
+ return RealGradient(ux, uy);
+ }
+
+ RealGradient operator() (Real x, Real y, Real z)
+ {
+ const Real ux = .5*pi*sin(.5*pi*x)*sin(.5*pi*y)*cos(.5*pi*z);
+ const Real uy = -.5*pi*cos(.5*pi*x)*cos(.5*pi*y)*cos(.5*pi*z);
+ const Real uz = .5*pi*cos(.5*pi*x)*sin(.5*pi*y)*sin(.5*pi*z);
+
+ return RealGradient(ux, uy, uz);
+ }
+
+ RealTensor grad(Real x, Real y)
+ {
+ const Real dux_dx = .5*pi*.5*pi*cos(.5*pi*x)*sin(.5*pi*y);
+ const Real dux_dy = .5*pi*.5*pi*sin(.5*pi*x)*cos(.5*pi*y);
+ const Real duy_dx = .5*pi*.5*pi*sin(.5*pi*x)*cos(.5*pi*y);
+ const Real duy_dy = .5*pi*.5*pi*cos(.5*pi*x)*sin(.5*pi*y);
+
+ return RealTensor(dux_dx, dux_dy, Real(0), duy_dx, duy_dy);
+ }
+
+ RealTensor grad(Real x, Real y, Real z)
+ {
+ const Real dux_dx = .5*pi*.5*pi*cos(.5*pi*x)*sin(.5*pi*y)*cos(.5*pi*z);
+ const Real dux_dy = .5*pi*.5*pi*sin(.5*pi*x)*cos(.5*pi*y)*cos(.5*pi*z);
+ const Real dux_dz = -.5*pi*.5*pi*sin(.5*pi*x)*sin(.5*pi*y)*sin(.5*pi*z);
+ const Real duy_dx = .5*pi*.5*pi*sin(.5*pi*x)*cos(.5*pi*y)*cos(.5*pi*z);
+ const Real duy_dy = .5*pi*.5*pi*cos(.5*pi*x)*sin(.5*pi*y)*cos(.5*pi*z);
+ const Real duy_dz = .5*pi*.5*pi*cos(.5*pi*x)*cos(.5*pi*y)*sin(.5*pi*z);
+ const Real duz_dx = -.5*pi*.5*pi*sin(.5*pi*x)*sin(.5*pi*y)*sin(.5*pi*z);
+ const Real duz_dy = .5*pi*.5*pi*cos(.5*pi*x)*cos(.5*pi*y)*sin(.5*pi*z);
+ const Real duz_dz = .5*pi*.5*pi*cos(.5*pi*x)*sin(.5*pi*y)*cos(.5*pi*z);
+
+ return RealTensor(dux_dx, dux_dy, dux_dz, duy_dx, duy_dy, duy_dz, duz_dx, duz_dy, duz_dz);
+ }
+
+ Real div(Real x, Real y)
+ {
+ const Real dux_dx = grad(x, y)(0, 0);
+ const Real duy_dy = grad(x, y)(1, 1);
+
+ return dux_dx + duy_dy;
+ }
+
+ Real div(Real x, Real y, Real z)
+ {
+ const Real dux_dx = grad(x, y, z)(0, 0);
+ const Real duy_dy = grad(x, y, z)(1, 1);
+ const Real duz_dz = grad(x, y, z)(2, 2);
+
+ return dux_dx + duy_dy + duz_dz;
+ }
+
+ Real forcing(Real x, Real y)
+ {
+ return div(x, y);
+ }
+
+ Real forcing(Real x, Real y, Real z)
+ {
+ return div(x, y, z);
+ }
+};
+
+#endif // DIV_GRAD_EXACT_SOLUTION_H
diff --git a/examples/vector_fe/vector_fe_ex6/run.sh b/examples/vector_fe/vector_fe_ex6/run.sh
new file mode 100755
index 00000000000..0548f310002
--- /dev/null
+++ b/examples/vector_fe/vector_fe_ex6/run.sh
@@ -0,0 +1,26 @@
+#!/bin/bash
+
+#set -x
+
+source $LIBMESH_DIR/examples/run_common.sh
+
+example_name=vector_fe_ex6
+
+options="dim=2 element_type=TRI6"
+run_example_no_extra_options "$example_name" "$options"
+
+options="dim=2 element_type=TRI7"
+run_example_no_extra_options "$example_name" "$options"
+
+options="dim=2 element_type=QUAD8"
+run_example_no_extra_options "$example_name" "$options"
+
+options="dim=2 element_type=QUAD9"
+run_example_no_extra_options "$example_name" "$options"
+
+# Subdividing each hex into 24 tets gets expensive in dbg...
+options="dim=3 element_type=TET14 grid_size=6"
+run_example_no_extra_options "$example_name" "$options"
+
+options="dim=3 element_type=HEX27"
+run_example_no_extra_options "$example_name" "$options"
diff --git a/examples/vector_fe/vector_fe_ex6/solution_function.h b/examples/vector_fe/vector_fe_ex6/solution_function.h
new file mode 100644
index 00000000000..fbb2435fcb1
--- /dev/null
+++ b/examples/vector_fe/vector_fe_ex6/solution_function.h
@@ -0,0 +1,179 @@
+// The libMesh Finite Element Library.
+// Copyright (C) 2002-2023 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
+
+// This library is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+// Lesser General Public License for more details.
+
+// You should have received a copy of the GNU Lesser General Public
+// License along with this library; if not, write to the Free Software
+// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+
+#ifndef SOLUTION_FUNCTION_H
+#define SOLUTION_FUNCTION_H
+
+// libMesh includes
+#include "libmesh/function_base.h"
+
+// Example includes
+#include "div_grad_exact_solution.h"
+
+// C++ includes
+#include
+
+using namespace libMesh;
+
+template
+class SolutionFunction : public FunctionBase
+{
+public:
+
+ SolutionFunction(const unsigned int u_var)
+ : _u_var(u_var) {}
+
+ ~SolutionFunction() = default;
+
+ virtual Number operator() (const Point &,
+ const Real = 0)
+ { libmesh_not_implemented(); }
+
+ virtual void operator() (const Point & p,
+ const Real,
+ DenseVector & output);
+
+ virtual Number component(unsigned int component_in,
+ const Point & p,
+ const Real);
+
+ virtual std::unique_ptr> clone() const
+ { return std::make_unique(_u_var); }
+
+private:
+
+ const unsigned int _u_var;
+ DivGradExactSolution soln;
+};
+
+template<>
+void SolutionFunction<2>::operator() (const Point & p,
+ const Real,
+ DenseVector & output)
+{
+ output.zero();
+ const Real x=p(0), y=p(1);
+ // libMesh assumes each component of the vector-valued variable is stored
+ // contiguously.
+ output(_u_var) = soln(x, y)(0);
+ output(_u_var+1) = soln(x, y)(1);
+}
+
+template<>
+void SolutionFunction<3>::operator() (const Point & p,
+ const Real,
+ DenseVector & output)
+{
+ output.zero();
+ const Real x=p(0), y=p(1), z=p(2);
+ // libMesh assumes each component of the vector-valued variable is stored
+ // contiguously.
+ output(_u_var) = soln(x, y, z)(0);
+ output(_u_var+1) = soln(x, y, z)(1);
+ output(_u_var+2) = soln(x, y, z)(2);
+}
+
+template<>
+Number SolutionFunction<2>::component(unsigned int component_in,
+ const Point & p,
+ const Real)
+{
+ const Real x=p(0), y=p(1);
+ return soln(x, y)(component_in);
+}
+
+template<>
+Number SolutionFunction<3>::component(unsigned int component_in,
+ const Point & p,
+ const Real)
+{
+ const Real x=p(0), y=p(1), z=p(2);
+ return soln(x, y, z)(component_in);
+}
+
+template
+class SolutionGradient : public FunctionBase
+{
+public:
+
+ SolutionGradient(const unsigned int u_var)
+ : _u_var(u_var) {}
+
+ ~SolutionGradient() = default;
+
+ virtual Gradient operator() (const Point &, const Real = 0)
+ { libmesh_not_implemented(); }
+
+ virtual void operator() (const Point & p,
+ const Real,
+ DenseVector & output);
+
+ virtual Gradient component(unsigned int component_in,
+ const Point & p,
+ const Real);
+
+ virtual std::unique_ptr> clone() const
+ { return std::make_unique(_u_var); }
+
+private:
+
+ const unsigned int _u_var;
+ DivGradExactSolution soln;
+};
+
+template<>
+void SolutionGradient<2>::operator() (const Point & p,
+ const Real,
+ DenseVector & output)
+{
+ output.zero();
+ const Real x=p(0), y=p(1);
+ output(_u_var) = soln.grad(x, y).row(0);
+ output(_u_var+1) = soln.grad(x, y).row(1);
+}
+
+template<>
+void SolutionGradient<3>::operator() (const Point & p,
+ const Real,
+ DenseVector & output)
+{
+ output.zero();
+ const Real x=p(0), y=p(1), z=p(2);
+ output(_u_var) = soln.grad(x, y, z).row(0);
+ output(_u_var+1) = soln.grad(x, y, z).row(1);
+ output(_u_var+2) = soln.grad(x, y, z).row(2);
+}
+
+template<>
+Gradient SolutionGradient<2>::component(unsigned int component_in,
+ const Point & p,
+ const Real)
+{
+ const Real x=p(0), y=p(1);
+ return soln.grad(x, y).row(component_in);
+}
+
+template<>
+Gradient SolutionGradient<3>::component(unsigned int component_in,
+ const Point & p,
+ const Real)
+{
+ const Real x=p(0), y=p(1), z=p(2);
+ return soln.grad(x, y, z).row(component_in);
+}
+
+#endif // SOLUTION_FUNCTION_H
diff --git a/examples/vector_fe/vector_fe_ex6/vector_fe_ex6.C b/examples/vector_fe/vector_fe_ex6/vector_fe_ex6.C
new file mode 100644
index 00000000000..3e4ef78873a
--- /dev/null
+++ b/examples/vector_fe/vector_fe_ex6/vector_fe_ex6.C
@@ -0,0 +1,575 @@
+// The libMesh Finite Element Library.
+// Copyright (C) 2002-2023 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
+
+// This library is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+// Lesser General Public License for more details.
+
+// You should have received a copy of the GNU Lesser General Public
+// License along with this library; if not, write to the Free Software
+// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+
+
+// Vector Finite Elements Example 6 - Raviart-Thomas elements
+// \author Nuno Nobre
+// \date 2023
+//
+// This example uses Raviart-Thomas elements to solve a model div-grad problem
+// in H(div) in both 2d and 3d. The problem is simply a div-grad formulation,
+// \vec{u} = -\nabla p, and \nabla \cdot \vec{u} = f, of the Poisson
+// problem in Introduction Example 3, \nabla^2 p = -f.
+
+// Basic utilities.
+#include "libmesh/string_to_enum.h"
+
+// The solver packages supported by libMesh.
+#include "libmesh/enum_solver_package.h"
+
+// The mesh object and mesh generation utilities.
+#include "libmesh/mesh.h"
+#include "libmesh/mesh_generation.h"
+
+// Matrix and vector types.
+#include "libmesh/dense_matrix.h"
+#include "libmesh/sparse_matrix.h"
+#include "libmesh/dense_vector.h"
+#include "libmesh/numeric_vector.h"
+
+// The finite element object and the geometric element type.
+#include "libmesh/fe.h"
+#include "libmesh/elem.h"
+
+// Gauss quadrature rules.
+#include "libmesh/quadrature_gauss.h"
+
+// The dof map, which handles degree of freedom indexing.
+#include "libmesh/dof_map.h"
+
+// The system of equations.
+#include "libmesh/equation_systems.h"
+#include "libmesh/linear_implicit_system.h"
+
+// The exact solution and error computation.
+#include "libmesh/exact_solution.h"
+#include "libmesh/enum_norm_type.h"
+#include "solution_function.h"
+
+// I/O utilities.
+#include "libmesh/getpot.h"
+#include "libmesh/exodusII_io.h"
+
+
+// Bring in everything from the libMesh namespace.
+using namespace libMesh;
+
+// Function prototype. This is the function that will assemble
+// the linear system for our div-grad problem. Note that the
+// function will take the EquationSystems object and the
+// name of the system we are assembling as input. From the
+// EquationSystems object we have access to the Mesh and
+// other objects we might need.
+void assemble_divgrad(EquationSystems & es,
+ const std::string & system_name);
+
+int main (int argc, char ** argv)
+{
+ // Initialize libMesh.
+ LibMeshInit init (argc, argv);
+
+ // This example requires a linear solver package.
+ libmesh_example_requires(libMesh::default_solver_package() != INVALID_SOLVER_PACKAGE,
+ "--enable-petsc, --enable-trilinos, or --enable-eigen");
+
+ // Parse the input file.
+ GetPot infile("vector_fe_ex6.in");
+
+ // But allow the command line to override it.
+ infile.parse_command_line(argc, argv);
+
+ // Read in parameters from the command line and the input file.
+ const unsigned int dimension = infile("dim", 2);
+ const unsigned int grid_size = infile("grid_size", 15);
+
+ // Skip higher-dimensional examples on a lower-dimensional libMesh build.
+ libmesh_example_requires(dimension <= LIBMESH_DIM, dimension << "D support");
+
+ // Create a mesh, with dimension to be overridden later, distributed
+ // across the default MPI communicator.
+ Mesh mesh(init.comm());
+
+ // Use the MeshTools::Generation mesh generator to create a uniform
+ // grid on the cube [-1,1]^D. To accomodate Raviart-Thomas elements, we must
+ // use TRI6/7 or QUAD8/9 elements in 2d, or TET14 or HEX27 in 3d.
+ const std::string elem_str = infile("element_type", std::string("TRI6"));
+
+ libmesh_error_msg_if((dimension == 2 && elem_str != "TRI6" && elem_str != "TRI7" && elem_str != "QUAD8" && elem_str != "QUAD9") ||
+ (dimension == 3 && elem_str != "TET14" && elem_str != "HEX27"),
+ "You selected " << elem_str <<
+ " but this example must be run with TRI6, TRI7, QUAD8, or QUAD9 in 2d" <<
+ " or with TET14, or HEX27 in 3d.");
+
+ if (dimension == 2)
+ MeshTools::Generation::build_square (mesh,
+ grid_size,
+ grid_size,
+ -1., 1.,
+ -1., 1.,
+ Utility::string_to_enum(elem_str));
+ else if (dimension == 3)
+ MeshTools::Generation::build_cube (mesh,
+ grid_size,
+ grid_size,
+ grid_size,
+ -1., 1.,
+ -1., 1.,
+ -1., 1.,
+ Utility::string_to_enum(elem_str));
+
+ // Print information about the mesh to the screen.
+ mesh.print_info();
+
+ // Create an equation systems object.
+ EquationSystems equation_systems (mesh);
+
+ // Declare the system "DivGrad" and its variables.
+ LinearImplicitSystem & system = equation_systems.add_system("DivGrad");
+
+ // Adds the variable "u" and "p" to "DivGrad". "u" will be our vector field
+ // whereas "p" will be the scalar field.
+ system.add_variable("u", FIRST, RAVIART_THOMAS);
+ system.add_variable("p", CONSTANT, MONOMIAL);
+
+ // Add a scalar Lagrange multiplier to enforce our constraint
+ system.add_variable("l", FIRST, SCALAR);
+
+ // Give the system a pointer to the matrix assembly
+ // function. This will be called when needed by the library.
+ system.attach_assemble_function(assemble_divgrad);
+
+ // Initialize the data structures for the equation system.
+ equation_systems.init();
+
+ // Prints information about the system to the screen.
+ equation_systems.print_info();
+
+ // Solve the system "DivGrad". Note that calling this
+ // member will assemble the linear system and invoke
+ // the default numerical solver.
+ system.solve();
+
+ ExactSolution exact_sol(equation_systems);
+
+ if (dimension == 2)
+ {
+ SolutionFunction<2> soln_func(system.variable_number("u"));
+ SolutionGradient<2> soln_grad(system.variable_number("u"));
+
+ // Build FunctionBase* containers to attach to the ExactSolution object.
+ std::vector *> sols(1, &soln_func);
+ std::vector *> grads(1, &soln_grad);
+
+ exact_sol.attach_exact_values(sols);
+ exact_sol.attach_exact_derivs(grads);
+ }
+ else if (dimension == 3)
+ {
+ SolutionFunction<3> soln_func(system.variable_number("u"));
+ SolutionGradient<3> soln_grad(system.variable_number("u"));
+
+ // Build FunctionBase* containers to attach to the ExactSolution object.
+ std::vector *> sols(1, &soln_func);
+ std::vector *> grads(1, &soln_grad);
+
+ exact_sol.attach_exact_values(sols);
+ exact_sol.attach_exact_derivs(grads);
+ }
+
+ // Use higher quadrature order for more accurate error results.
+ int extra_error_quadrature = infile("extra_error_quadrature", 2);
+ exact_sol.extra_quadrature_order(extra_error_quadrature);
+
+ // Compute the error.
+ exact_sol.compute_error("DivGrad", "u");
+
+ // Print out the error values.
+ libMesh::out << "L2 error is: "
+ << exact_sol.l2_error("DivGrad", "u")
+ << std::endl;
+ libMesh::out << "HDiv semi-norm error is: "
+ << exact_sol.error_norm("DivGrad", "u", HDIV_SEMINORM)
+ << std::endl;
+ libMesh::out << "HDiv error is: "
+ << exact_sol.hdiv_error("DivGrad", "u")
+ << std::endl;
+
+#ifdef LIBMESH_HAVE_EXODUS_API
+
+ // We write the file in the ExodusII format.
+ ExodusII_IO(mesh).write_equation_systems("out.e", equation_systems);
+
+#endif // #ifdef LIBMESH_HAVE_EXODUS_API
+
+ // All done.
+ return 0;
+}
+
+
+
+// We now define the matrix assembly function for the
+// div-grad system. We need to first compute element
+// matrices and right-hand sides, and then take into
+// account the boundary conditions, which will be handled
+// via a penalty method.
+void assemble_divgrad(EquationSystems & es,
+ const std::string & libmesh_dbg_var(system_name))
+{
+
+ // It is a good idea to make sure we are assembling
+ // the proper system.
+ libmesh_assert_equal_to (system_name, "DivGrad");
+
+ // Get a constant reference to the mesh object.
+ const MeshBase & mesh = es.get_mesh();
+
+ // The dimension that we are running.
+ const unsigned int dim = mesh.mesh_dimension();
+
+ // Get a reference to the LinearImplicitSystem we are solving.
+ LinearImplicitSystem & system = es.get_system("DivGrad");
+
+ // A reference to the DofMap object for this system. The DofMap
+ // object handles the index translation from node and element numbers
+ // to degree of freedom numbers.
+ const DofMap & dof_map = system.get_dof_map();
+
+ // Get a constant reference to the Finite Element type
+ // for the two variables in the system.
+ FEType vector_fe_type = dof_map.variable_type(system.variable_number("u"));
+ FEType scalar_fe_type = dof_map.variable_type(system.variable_number("p"));
+
+ // Build two Finite Element objects, one of each specified type. Since the
+ // FEBase::build() member dynamically creates memory we will
+ // store the object as a std::unique_ptr. This can be thought
+ // of as a pointer that will clean up after itself. Introduction Example 4
+ // describes some advantages of std::unique_ptr's in the context of
+ // quadrature rules.
+ std::unique_ptr vector_fe (FEVectorBase::build(dim, vector_fe_type));
+ std::unique_ptr scalar_fe (FEBase::build(dim, scalar_fe_type));
+
+ // A 5th order Gauss quadrature rule for numerical integration.
+ QGauss qrule (dim, FIFTH);
+
+ // Tell the finite element objects to use our quadrature rule.
+ vector_fe->attach_quadrature_rule (&qrule);
+ scalar_fe->attach_quadrature_rule (&qrule);
+
+ // Declare a special finite element object for boundary integration.
+ std::unique_ptr vector_fe_face (FEVectorBase::build(dim, vector_fe_type));
+
+ // Boundary integration requires one quadrature rule with dimensionality one
+ // less than the dimensionality of the element.
+ QGauss qface(dim-1, FIFTH);
+
+ // Tell the finite element object to use our quadrature rule.
+ vector_fe_face->attach_quadrature_rule (&qface);
+
+ // Here we define some references to cell-specific data that
+ // will be used to assemble the linear system.
+ //
+ // The element Jacobian * quadrature weight at each integration point.
+ const std::vector & JxW = vector_fe->get_JxW();
+
+ // The physical XY locations of the quadrature points on the element.
+ // These might be useful for evaluating spatially varying material
+ // properties at the quadrature points.
+ const std::vector & q_point = vector_fe->get_xyz();
+
+ // The element shape functions evaluated at the quadrature points.
+ const std::vector> & vector_phi = vector_fe->get_phi();
+ const std::vector> & scalar_phi = scalar_fe->get_phi();
+
+ // The divergence of the element vector shape functions evaluated at the
+ // quadrature points.
+ const std::vector> & div_vector_phi = vector_fe->get_div_phi();
+
+ // Define data structures to contain the element matrix
+ // and right-hand-side vector contribution. Following
+ // basic finite element terminology we will denote these
+ // "Ke" and "Fe". These datatypes are templated on
+ // Number, which allows the same code to work for real
+ // or complex numbers.
+ DenseMatrix Ke;
+ DenseVector Fe;
+
+ // These vectors will hold the degree of freedom indices for
+ // the element. These define where in the global system
+ // the element degrees of freedom get mapped.
+ std::vector dof_indices;
+ std::vector vector_dof_indices;
+ std::vector scalar_dof_indices;
+ std::vector lambda_dof_indices;
+
+ // The global system matrix
+ SparseMatrix & matrix = system.get_system_matrix();
+
+ // Now we will loop over all the elements in the mesh.
+ // We will compute the element matrix and right-hand-side
+ // contribution.
+ //
+ // Element ranges are a nice way to iterate through all the
+ // elements, or all the elements that have some property. The
+ // range will iterate from the first to the last element on
+ // the local processor.
+ // It is smart to make this one const so that we don't accidentally
+ // mess it up! In case users later modify this program to include
+ // refinement, we will be safe and will only consider the active
+ // elements; hence we use a variant of the
+ // active_local_element_ptr_range.
+ for (const auto & elem : mesh.active_local_element_ptr_range())
+ {
+ // Get the degree of freedom indices for the
+ // current element. These define where in the global
+ // matrix and right-hand-side this element will
+ // contribute to.
+ dof_map.dof_indices (elem, dof_indices);
+ dof_map.dof_indices (elem, vector_dof_indices, system.variable_number("u"));
+ dof_map.dof_indices (elem, scalar_dof_indices, system.variable_number("p"));
+ dof_map.dof_indices (elem, lambda_dof_indices, system.variable_number("l"));
+
+ // Cache the number of degrees of freedom, in total and for each
+ // variable, on this element, for use as array and loop bounds later.
+ // We use cast_int to explicitly convert from size() (which may be
+ // 64-bit) to unsigned int (which may be 32-bit but which is definitely
+ // enough to count *local* degrees of freedom.
+ const unsigned int n_dofs =
+ cast_int(dof_indices.size());
+ const unsigned int vector_n_dofs =
+ cast_int(vector_dof_indices.size());
+ const unsigned int scalar_n_dofs =
+ cast_int(scalar_dof_indices.size());
+ const unsigned int lambda_n_dofs =
+ cast_int(lambda_dof_indices.size());
+
+ // Compute the element-specific data for the current
+ // element. This involves computing the location of the
+ // quadrature points (q_point) and the shape functions
+ // and their divergences for the current element.
+ vector_fe->reinit (elem);
+ scalar_fe->reinit (elem);
+
+ // The total number of degrees of freedom is just the sum of the number
+ // of degrees of freedom per variable. We should also have the same
+ // number of degrees of freedom as shape functions for each variable.
+ libmesh_assert_equal_to (n_dofs, vector_n_dofs + scalar_n_dofs + lambda_n_dofs);
+ libmesh_assert_equal_to (vector_n_dofs, vector_phi.size());
+ libmesh_assert_equal_to (scalar_n_dofs, scalar_phi.size());
+
+ // Zero the element matrix and right-hand side before
+ // summing them. We use the resize member here because
+ // the number of degrees of freedom might have changed from
+ // the last element. Note that this will be the case if the
+ // element type is different (i.e. the last element was a
+ // triangle, now we are on a quadrilateral).
+
+ // The DenseMatrix::resize() and the DenseVector::resize()
+ // members will automatically zero out the matrix and vector.
+ Ke.resize (n_dofs, n_dofs);
+ Fe.resize (n_dofs);
+
+ // Now loop over the quadrature points. This handles
+ // the numeric integration.
+ for (unsigned int qp=0; qpside_index_range())
+ if (elem->neighbor_ptr(side) == nullptr)
+ {
+ // The value of the shape functions at the quadrature points.
+ const std::vector> & vector_phi_face = vector_fe_face->get_phi();
+
+ // The Jacobian * Quadrature Weight at the quadrature
+ // points on the face.
+ const std::vector & JxW_face = vector_fe_face->get_JxW();
+
+ // The XYZ locations (in physical space) of, and the normals at,
+ // the quadrature points on the face. This is where
+ // we will interpolate the boundary value function.
+ const std::vector & qface_point = vector_fe_face->get_xyz();
+ const std::vector & normals = vector_fe_face->get_normals();
+
+ // Compute the vector shape function values on the element face.
+ vector_fe_face->reinit(elem, side);
+
+ // Some shape functions will be 0 on the face, but for ease of
+ // indexing and generality of code we loop over them anyway.
+ libmesh_assert_equal_to (vector_n_dofs, vector_phi_face.size());
+
+ // Loop over the face quadrature points for integration.
+ for (unsigned int qp=0; qpadd_vector (Fe, dof_indices);
+ }
+
+ // All done!
+}
diff --git a/examples/vector_fe/vector_fe_ex6/vector_fe_ex6.in b/examples/vector_fe/vector_fe_ex6/vector_fe_ex6.in
new file mode 100644
index 00000000000..656a9df3e08
--- /dev/null
+++ b/examples/vector_fe/vector_fe_ex6/vector_fe_ex6.in
@@ -0,0 +1,11 @@
+# Solve the 2D or 3D problem
+dim = 2
+
+# The element type
+element_type = TRI6
+
+# The coarse grid size from which to start adaptivity
+grid_size = 15
+
+# Higher quadrature order for more accurate error results
+extra_error_quadrature = 0
diff --git a/include/Makefile.in b/include/Makefile.in
index bf3d543840f..53148f25447 100644
--- a/include/Makefile.in
+++ b/include/Makefile.in
@@ -687,6 +687,7 @@ include_HEADERS = \
fe/fe_xyz_map.h \
fe/h1_fe_transformation.h \
fe/hcurl_fe_transformation.h \
+ fe/hdiv_fe_transformation.h \
fe/inf_fe.h \
fe/inf_fe_instantiate_1D.h \
fe/inf_fe_instantiate_2D.h \
diff --git a/include/base/libmesh_documentation.h b/include/base/libmesh_documentation.h
index 84b3333758f..3637119ec30 100644
--- a/include/base/libmesh_documentation.h
+++ b/include/base/libmesh_documentation.h
@@ -40,7 +40,7 @@
* - Hierarchic
* - C1 elements (Hermite, Clough-Tocher)
* - Discontinuous elements (Monomials, L2-Lagrange)
- * - Vector-valued elements (Lagrange-Vec, Monomial-Vec, Nedelec first type)
+ * - Vector-valued elements (Lagrange-Vec, Monomial-Vec, Nedelec first type, Raviart-Thomas)
*
* - Dimension-independence
* - Operators are defined to allow the same code to run unmodified on 2D and 3D applications.
diff --git a/include/enums/enum_fe_family.h b/include/enums/enum_fe_family.h
index dcdcd30a639..797d2b2cb40 100644
--- a/include/enums/enum_fe_family.h
+++ b/include/enums/enum_fe_family.h
@@ -57,9 +57,10 @@ enum FEFamily : int {
// all other DOFs in the system
SCALAR = 31,
// Vector-valued elements
- LAGRANGE_VEC = 41,
- NEDELEC_ONE = 42,
- MONOMIAL_VEC = 43,
+ LAGRANGE_VEC = 41,
+ NEDELEC_ONE = 42,
+ MONOMIAL_VEC = 43,
+ RAVIART_THOMAS = 44,
// Rational basis functions
RATIONAL_BERNSTEIN = 61,
// Side-supported basis functions
@@ -81,6 +82,7 @@ enum FEContinuity : int {
C_ZERO,
C_ONE,
H_CURL,
+ H_DIV,
SIDE_DISCONTINUOUS};
/**
diff --git a/include/fe/fe.h b/include/fe/fe.h
index 3a3940afaae..03333b580e7 100644
--- a/include/fe/fe.h
+++ b/include/fe/fe.h
@@ -75,6 +75,12 @@ struct FEOutputType
typedef RealVectorValue type;
};
+template<>
+struct FEOutputType
+{
+ typedef RealVectorValue type;
+};
+
/**
* A specific instantiation of the \p FEBase class. This
@@ -1209,7 +1215,27 @@ class FEMonomialVec : public FE
{}
};
+/**
+ * FERaviartThomas objects are used for working with vector-valued
+ * Raviart-Thomas finite elements.
+ *
+ * \author Nuno Nobre & Karthikeyan Chockalingam
+ * \date 2023
+ */
+template
+class FERaviartThomas : public FE
+{
+public:
+ /**
+ * Constructor. Creates a Raviart-Thomas finite element
+ * to be used in dimension \p Dim.
+ */
+ explicit
+ FERaviartThomas(const FEType & fet) :
+ FE (fet)
+ {}
+};
/**
* Provide Typedefs for various element types.
diff --git a/include/fe/fe_macro.h b/include/fe/fe_macro.h
index ac37ee926a9..8e6910de7f3 100644
--- a/include/fe/fe_macro.h
+++ b/include/fe/fe_macro.h
@@ -84,7 +84,8 @@
template class LIBMESH_EXPORT FE< (_dim), SIDE_HIERARCHIC>; \
template class LIBMESH_EXPORT FE< (_dim), XYZ>; \
template class LIBMESH_EXPORT FE< (_dim), NEDELEC_ONE>; \
- template class LIBMESH_EXPORT FE< (_dim), MONOMIAL_VEC>
+ template class LIBMESH_EXPORT FE< (_dim), MONOMIAL_VEC>; \
+ template class LIBMESH_EXPORT FE< (_dim), RAVIART_THOMAS>
#else //LIBMESH_ENABLE_HIGHER_ORDER_SHAPES
@@ -104,7 +105,8 @@
template class LIBMESH_EXPORT FE< (_dim), XYZ>; \
template class LIBMESH_EXPORT FE< (_dim), RATIONAL_BERNSTEIN>; \
template class LIBMESH_EXPORT FE< (_dim), NEDELEC_ONE>; \
- template class LIBMESH_EXPORT FE< (_dim), MONOMIAL_VEC>
+ template class LIBMESH_EXPORT FE< (_dim), MONOMIAL_VEC>; \
+ template class LIBMESH_EXPORT FE< (_dim), RAVIART_THOMAS>
#endif //LIBMESH_ENABLE_HIGHER_ORDER_SHAPES
diff --git a/include/fe/fe_transformation_base.h b/include/fe/fe_transformation_base.h
index 5a746afa6bf..be823050d8b 100644
--- a/include/fe/fe_transformation_base.h
+++ b/include/fe/fe_transformation_base.h
@@ -27,6 +27,7 @@ namespace libMesh
template class FEGenericBase;
template class H1FETransformation;
template class HCurlFETransformation;
+template class HDivFETransformation;
class FEType;
/**
diff --git a/include/fe/hdiv_fe_transformation.h b/include/fe/hdiv_fe_transformation.h
new file mode 100644
index 00000000000..73660da68f2
--- /dev/null
+++ b/include/fe/hdiv_fe_transformation.h
@@ -0,0 +1,140 @@
+// The libMesh Finite Element Library.
+// Copyright (C) 2002-2023 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
+
+// This library is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+// Lesser General Public License for more details.
+
+// You should have received a copy of the GNU Lesser General Public
+// License along with this library; if not, write to the Free Software
+// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+
+#ifndef LIBMESH_HDIV_FE_TRANSFORMATION_H
+#define LIBMESH_HDIV_FE_TRANSFORMATION_H
+
+#include "libmesh/fe_transformation_base.h"
+
+namespace libMesh
+{
+
+/**
+ * This class handles the computation of the shape functions in the
+ * physical domain for HDiv conforming elements. This class assumes
+ * the \p FEGenericBase object has been initialized in the reference
+ * domain (i.e. \p init_shape_functions has been called).
+ *
+ * \author Nuno Nobre
+ * \date 2023
+ */
+template
+class HDivFETransformation : public FETransformationBase
+{
+public:
+
+ HDivFETransformation()
+ : FETransformationBase() {}
+
+ virtual ~HDivFETransformation() = default;
+
+ /**
+ * Pre-requests any necessary data from FEMap
+ */
+ virtual void init_map_phi(const FEGenericBase & fe) const override;
+
+ /**
+ * Pre-requests any necessary data from FEMap
+ */
+ virtual void init_map_dphi(const FEGenericBase & fe) const override;
+
+ /**
+ * Pre-requests any necessary data from FEMap
+ */
+ virtual void init_map_d2phi(const FEGenericBase & fe) const override;
+
+ /**
+ * Evaluates shape functions in physical coordinates for \f$ H(div)
+ * \f$ conforming elements. In this case \f$ \phi = J^{-1} (dx/d\xi)
+ * \hat{\phi} \f$, where \f$ (dx/d\xi) \f$ is the Jacobian matrix of the
+ * element map and J = \det( dx/d\xi ).
+ *
+ * \note Here \f$ x, \xi \f$ are vectors.
+ */
+ virtual void map_phi(const unsigned int dim,
+ const Elem * const elem,
+ const std::vector & qp,
+ const FEGenericBase & fe,
+ std::vector> & phi,
+ bool add_p_level = true) const override;
+
+ /**
+ * Evaluates shape function gradients in physical coordinates for
+ * \f$ H(div) \f$ conforming elements.
+ */
+ virtual void map_dphi(const unsigned int /*dim*/,
+ const Elem * const /*elem*/,
+ const std::vector & /*qp*/,
+ const FEGenericBase & /*fe*/,
+ std::vector::OutputGradient>> & /*dphi*/,
+ std::vector> & /*dphidx*/,
+ std::vector> & /*dphidy*/,
+ std::vector> & /*dphidz*/) const override
+ {
+ libmesh_warning("WARNING: Shape function gradients for HDiv elements are not currently being computed!");
+ }
+
+#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
+ /**
+ * Evaluates shape function Hessians in physical coordinates based
+ * on \f$ H(div) \f$ conforming finite element transformation.
+ */
+ virtual void map_d2phi(const unsigned int /*dim*/,
+ const std::vector & /*qp*/,
+ const FEGenericBase & /*fe*/,
+ std::vector::OutputTensor>> & /*d2phi*/,
+ std::vector> & /*d2phidx2*/,
+ std::vector> & /*d2phidxdy*/,
+ std::vector> & /*d2phidxdz*/,
+ std::vector> & /*d2phidy2*/,
+ std::vector> & /*d2phidydz*/,
+ std::vector> & /*d2phidz2*/) const override
+ {
+ libmesh_warning("WARNING: Shape function Hessians for HDiv elements are not currently being computed!");
+ }
+#endif //LIBMESH_ENABLE_SECOND_DERIVATIVES
+
+ /**
+ * Evaluates the shape function curl in physical coordinates
+ * based on \f$ H(div) \f$ conforming finite element transformation.
+ */
+ virtual void map_curl(const unsigned int /*dim*/,
+ const Elem * const /*elem*/,
+ const std::vector & /*qp*/,
+ const FEGenericBase & /*fe*/,
+ std::vector> & /*curl_phi*/) const override
+ {
+ libmesh_warning("WARNING: Shape function curls for HDiv elements are not currently being computed!");
+ }
+
+ /**
+ * Evaluates the shape function divergence in physical coordinates based on \f$ H(div) \f$ conforming
+ * finite element transformation.
+ * The transformation is \f$ \nabla \cdot \phi = J^{-1} \nabla \cdot \hat{\phi} \f$ where
+ * \f$ J = \det( dx/d\xi ) \f$
+ */
+ virtual void map_div(const unsigned int dim,
+ const Elem * const elem,
+ const std::vector & qp,
+ const FEGenericBase & fe,
+ std::vector::OutputDivergence>> & div_phi) const override;
+
+}; // class HDivFETransformation
+
+}
+
+#endif // LIBMESH_HDIV_FE_TRANSFORMATION_H
diff --git a/include/include_HEADERS b/include/include_HEADERS
index 47a575cf42b..fbab4d62b67 100644
--- a/include/include_HEADERS
+++ b/include/include_HEADERS
@@ -93,6 +93,7 @@ include_HEADERS = \
fe/fe_xyz_map.h \
fe/h1_fe_transformation.h \
fe/hcurl_fe_transformation.h \
+ fe/hdiv_fe_transformation.h \
fe/inf_fe.h \
fe/inf_fe_instantiate_1D.h \
fe/inf_fe_instantiate_2D.h \
diff --git a/include/libmesh/Makefile.am b/include/libmesh/Makefile.am
index 522f498649d..b31b6f89c06 100644
--- a/include/libmesh/Makefile.am
+++ b/include/libmesh/Makefile.am
@@ -83,6 +83,7 @@ BUILT_SOURCES = \
fe_xyz_map.h \
h1_fe_transformation.h \
hcurl_fe_transformation.h \
+ hdiv_fe_transformation.h \
inf_fe.h \
inf_fe_instantiate_1D.h \
inf_fe_instantiate_2D.h \
@@ -820,6 +821,9 @@ h1_fe_transformation.h: $(top_srcdir)/include/fe/h1_fe_transformation.h
hcurl_fe_transformation.h: $(top_srcdir)/include/fe/hcurl_fe_transformation.h
$(AM_V_GEN)rm -f $@ && $(LN_S) -f $< $@
+hdiv_fe_transformation.h: $(top_srcdir)/include/fe/hdiv_fe_transformation.h
+ $(AM_V_GEN)rm -f $@ && $(LN_S) -f $< $@
+
inf_fe.h: $(top_srcdir)/include/fe/inf_fe.h
$(AM_V_GEN)rm -f $@ && $(LN_S) -f $< $@
diff --git a/include/libmesh/Makefile.in b/include/libmesh/Makefile.in
index 4eda43a0e4e..83579902454 100644
--- a/include/libmesh/Makefile.in
+++ b/include/libmesh/Makefile.in
@@ -540,33 +540,33 @@ BUILT_SOURCES = auto_ptr.h dirichlet_boundaries.h dof_map.h \
fe_base.h fe_compute_data.h fe_interface.h \
fe_interface_macros.h fe_lagrange_shape_1D.h fe_macro.h \
fe_map.h fe_transformation_base.h fe_type.h fe_xyz_map.h \
- h1_fe_transformation.h hcurl_fe_transformation.h inf_fe.h \
- inf_fe_instantiate_1D.h inf_fe_instantiate_2D.h \
- inf_fe_instantiate_3D.h inf_fe_macro.h inf_fe_map.h \
- bounding_box.h cell.h cell_hex.h cell_hex20.h cell_hex27.h \
- cell_hex8.h cell_inf.h cell_inf_hex.h cell_inf_hex16.h \
- cell_inf_hex18.h cell_inf_hex8.h cell_inf_prism.h \
- cell_inf_prism12.h cell_inf_prism6.h cell_prism.h \
- cell_prism15.h cell_prism18.h cell_prism20.h cell_prism21.h \
- cell_prism6.h cell_pyramid.h cell_pyramid13.h cell_pyramid14.h \
- cell_pyramid18.h cell_pyramid5.h cell_tet.h cell_tet10.h \
- cell_tet14.h cell_tet4.h compare_elems_by_level.h edge.h \
- edge_edge2.h edge_edge3.h edge_edge4.h edge_inf_edge2.h elem.h \
- elem_cutter.h elem_hash.h elem_internal.h elem_quality.h \
- elem_range.h elem_side_builder.h face.h face_inf_quad.h \
- face_inf_quad4.h face_inf_quad6.h face_quad.h face_quad4.h \
- face_quad4_shell.h face_quad8.h face_quad8_shell.h \
- face_quad9.h face_tri.h face_tri3.h face_tri3_shell.h \
- face_tri3_subdivision.h face_tri6.h face_tri7.h node.h \
- node_elem.h node_range.h plane.h point.h reference_elem.h \
- remote_elem.h side.h sphere.h stored_range.h surface.h \
- default_coupling.h ghost_point_neighbors.h ghosting_functor.h \
- point_neighbor_coupling.h sibling_coupling.h abaqus_io.h \
- boundary_info.h boundary_mesh.h checkpoint_io.h \
- distributed_mesh.h dyna_io.h ensight_io.h exodusII_io.h \
- exodusII_io_helper.h exodus_header_info.h fro_io.h gmsh_io.h \
- gmv_io.h gnuplot_io.h inf_elem_builder.h matlab_io.h \
- medit_io.h mesh.h mesh_base.h mesh_communication.h \
+ h1_fe_transformation.h hcurl_fe_transformation.h \
+ hdiv_fe_transformation.h inf_fe.h inf_fe_instantiate_1D.h \
+ inf_fe_instantiate_2D.h inf_fe_instantiate_3D.h inf_fe_macro.h \
+ inf_fe_map.h bounding_box.h cell.h cell_hex.h cell_hex20.h \
+ cell_hex27.h cell_hex8.h cell_inf.h cell_inf_hex.h \
+ cell_inf_hex16.h cell_inf_hex18.h cell_inf_hex8.h \
+ cell_inf_prism.h cell_inf_prism12.h cell_inf_prism6.h \
+ cell_prism.h cell_prism15.h cell_prism18.h cell_prism20.h \
+ cell_prism21.h cell_prism6.h cell_pyramid.h cell_pyramid13.h \
+ cell_pyramid14.h cell_pyramid18.h cell_pyramid5.h cell_tet.h \
+ cell_tet10.h cell_tet14.h cell_tet4.h compare_elems_by_level.h \
+ edge.h edge_edge2.h edge_edge3.h edge_edge4.h edge_inf_edge2.h \
+ elem.h elem_cutter.h elem_hash.h elem_internal.h \
+ elem_quality.h elem_range.h elem_side_builder.h face.h \
+ face_inf_quad.h face_inf_quad4.h face_inf_quad6.h face_quad.h \
+ face_quad4.h face_quad4_shell.h face_quad8.h \
+ face_quad8_shell.h face_quad9.h face_tri.h face_tri3.h \
+ face_tri3_shell.h face_tri3_subdivision.h face_tri6.h \
+ face_tri7.h node.h node_elem.h node_range.h plane.h point.h \
+ reference_elem.h remote_elem.h side.h sphere.h stored_range.h \
+ surface.h default_coupling.h ghost_point_neighbors.h \
+ ghosting_functor.h point_neighbor_coupling.h \
+ sibling_coupling.h abaqus_io.h boundary_info.h boundary_mesh.h \
+ checkpoint_io.h distributed_mesh.h dyna_io.h ensight_io.h \
+ exodusII_io.h exodusII_io_helper.h exodus_header_info.h \
+ fro_io.h gmsh_io.h gmv_io.h gnuplot_io.h inf_elem_builder.h \
+ matlab_io.h medit_io.h mesh.h mesh_base.h mesh_communication.h \
mesh_function.h mesh_generation.h mesh_input.h \
mesh_inserter_iterator.h mesh_modification.h mesh_output.h \
mesh_refinement.h mesh_serializer.h mesh_smoother.h \
@@ -1155,6 +1155,9 @@ h1_fe_transformation.h: $(top_srcdir)/include/fe/h1_fe_transformation.h
hcurl_fe_transformation.h: $(top_srcdir)/include/fe/hcurl_fe_transformation.h
$(AM_V_GEN)rm -f $@ && $(LN_S) -f $< $@
+hdiv_fe_transformation.h: $(top_srcdir)/include/fe/hdiv_fe_transformation.h
+ $(AM_V_GEN)rm -f $@ && $(LN_S) -f $< $@
+
inf_fe.h: $(top_srcdir)/include/fe/inf_fe.h
$(AM_V_GEN)rm -f $@ && $(LN_S) -f $< $@
diff --git a/src/fe/fe_abstract.C b/src/fe/fe_abstract.C
index 8abe8e6125e..604a56e7972 100644
--- a/src/fe/fe_abstract.C
+++ b/src/fe/fe_abstract.C
@@ -248,6 +248,9 @@ std::unique_ptr FEAbstract::build(const unsigned int dim,
case NEDELEC_ONE:
return std::make_unique>(fet);
+ case RAVIART_THOMAS:
+ return std::make_unique>(fet);
+
case SUBDIVISION:
return std::make_unique(fet);
@@ -312,6 +315,9 @@ std::unique_ptr FEAbstract::build(const unsigned int dim,
case NEDELEC_ONE:
return std::make_unique>(fet);
+ case RAVIART_THOMAS:
+ return std::make_unique>(fet);
+
default:
libmesh_error_msg("ERROR: Bad FEType.family= " << Utility::enum_to_string(fet.family));
}
diff --git a/src/fe/fe_base.C b/src/fe/fe_base.C
index 819481b2a8a..d6b3138be0d 100644
--- a/src/fe/fe_base.C
+++ b/src/fe/fe_base.C
@@ -457,6 +457,9 @@ FEGenericBase::build (const unsigned int dim,
case NEDELEC_ONE:
return std::make_unique>(fet);
+ case RAVIART_THOMAS:
+ return std::make_unique>(fet);
+
default:
libmesh_error_msg("ERROR: Bad FEType.family == " << Utility::enum_to_string(fet.family));
}
@@ -474,6 +477,9 @@ FEGenericBase::build (const unsigned int dim,
case NEDELEC_ONE:
return std::make_unique>(fet);
+ case RAVIART_THOMAS:
+ return std::make_unique>(fet);
+
default:
libmesh_error_msg("ERROR: Bad FEType.family == " << Utility::enum_to_string(fet.family));
}
diff --git a/src/fe/fe_boundary.C b/src/fe/fe_boundary.C
index 5c75dff23e2..35af6df5509 100644
--- a/src/fe/fe_boundary.C
+++ b/src/fe/fe_boundary.C
@@ -81,6 +81,7 @@ LIBMESH_ERRORS_IN_LOW_D(LAGRANGE_VEC)
LIBMESH_ERRORS_IN_LOW_D(MONOMIAL)
LIBMESH_ERRORS_IN_LOW_D(MONOMIAL_VEC)
LIBMESH_ERRORS_IN_LOW_D(NEDELEC_ONE)
+LIBMESH_ERRORS_IN_LOW_D(RAVIART_THOMAS)
LIBMESH_ERRORS_IN_LOW_D(SCALAR)
LIBMESH_ERRORS_IN_LOW_D(XYZ)
@@ -93,7 +94,8 @@ LIBMESH_ERRORS_IN_LOW_D(RATIONAL_BERNSTEIN)
// Special error instantiations
REINIT_ERROR(1, NEDELEC_ONE, reinit) { libmesh_error_msg("ERROR: Cannot reinit 1D NEDELEC_ONE elements!"); }
SIDEMAP_ERROR(1, NEDELEC_ONE, side_map) { libmesh_error_msg("ERROR: Cannot side_map 1D NEDELEC_ONE elements!"); }
-
+REINIT_ERROR(1, RAVIART_THOMAS, reinit) { libmesh_error_msg("ERROR: Cannot reinit 1D RAVIART_THOMAS elements!"); }
+SIDEMAP_ERROR(1, RAVIART_THOMAS, side_map) { libmesh_error_msg("ERROR: Cannot side_map 1D RAVIART_THOMAS elements!"); }
//-------------------------------------------------------
// Methods for 2D, 3D
@@ -1147,16 +1149,27 @@ REINIT_AND_SIDE_MAPS(RATIONAL_BERNSTEIN);
template LIBMESH_EXPORT void FE<2,SUBDIVISION>::reinit(Elem const *, unsigned int, Real, const std::vector * const, const std::vector * const);
template LIBMESH_EXPORT void FE<2,SUBDIVISION>::edge_map(Elem const *, Elem const *, const unsigned int, const std::vector &, std::vector &);
+
template LIBMESH_EXPORT void FE<2,NEDELEC_ONE>::reinit(Elem const *, unsigned int, Real, const std::vector * const, const std::vector * const);
template LIBMESH_EXPORT void FE<2,NEDELEC_ONE>::side_map(Elem const *, Elem const *, const unsigned int, const std::vector &, std::vector &);
template LIBMESH_EXPORT void FE<2,NEDELEC_ONE>::edge_map(Elem const *, Elem const *, const unsigned int, const std::vector &, std::vector &);
template LIBMESH_EXPORT void FE<2,NEDELEC_ONE>::edge_reinit(Elem const *, unsigned int, Real, const std::vector * const, const std::vector * const);
+template LIBMESH_EXPORT void FE<2,RAVIART_THOMAS>::reinit(Elem const *, unsigned int, Real, const std::vector * const, const std::vector * const);
+template LIBMESH_EXPORT void FE<2,RAVIART_THOMAS>::side_map(Elem const *, Elem const *, const unsigned int, const std::vector &, std::vector &);
+template LIBMESH_EXPORT void FE<2,RAVIART_THOMAS>::edge_map(Elem const *, Elem const *, const unsigned int, const std::vector &, std::vector &);
+template LIBMESH_EXPORT void FE<2,RAVIART_THOMAS>::edge_reinit(Elem const *, unsigned int, Real, const std::vector * const, const std::vector * const);
+
template LIBMESH_EXPORT void FE<3,NEDELEC_ONE>::reinit(Elem const *, unsigned int, Real, const std::vector * const, const std::vector * const);
template LIBMESH_EXPORT void FE<3,NEDELEC_ONE>::side_map(Elem const *, Elem const *, const unsigned int, const std::vector &, std::vector &);
template LIBMESH_EXPORT void FE<3,NEDELEC_ONE>::edge_map(Elem const *, Elem const *, const unsigned int, const std::vector &, std::vector &);
template LIBMESH_EXPORT void FE<3,NEDELEC_ONE>::edge_reinit(Elem const *, unsigned int, Real, const std::vector * const, const std::vector * const);
+template LIBMESH_EXPORT void FE<3,RAVIART_THOMAS>::reinit(Elem const *, unsigned int, Real, const std::vector * const, const std::vector * const);
+template LIBMESH_EXPORT void FE<3,RAVIART_THOMAS>::side_map(Elem const *, Elem const *, const unsigned int, const std::vector &, std::vector &);
+template LIBMESH_EXPORT void FE<3,RAVIART_THOMAS>::edge_map(Elem const *, Elem const *, const unsigned int, const std::vector &, std::vector &);
+template LIBMESH_EXPORT void FE<3,RAVIART_THOMAS>::edge_reinit(Elem const *, unsigned int, Real, const std::vector * const, const std::vector * const);
+
// Intel 9.1 complained it needed this in devel mode.
//template LIBMESH_EXPORT void FE<2,XYZ>::init_face_shape_functions(const std::vector &, const Elem *);
//template LIBMESH_EXPORT void FE<3,XYZ>::init_face_shape_functions(const std::vector &, const Elem *);
diff --git a/src/fe/fe_interface.C b/src/fe/fe_interface.C
index 616ce3ec3b4..929adc83cbb 100644
--- a/src/fe/fe_interface.C
+++ b/src/fe/fe_interface.C
@@ -163,6 +163,8 @@ FEInterface::is_InfFE_elem(const ElemType et)
prefix FE<2,SUBDIVISION>::func_and_args suffix \
case NEDELEC_ONE: \
prefix FENedelecOne::func_and_args suffix \
+ case RAVIART_THOMAS: \
+ prefix FERaviartThomas::func_and_args suffix \
default: \
libmesh_error_msg("Unsupported family = " << Utility::enum_to_string(fe_t.family)); \
} \
@@ -204,6 +206,7 @@ FEInterface::is_InfFE_elem(const ElemType et)
case LAGRANGE_VEC: \
case NEDELEC_ONE: \
case MONOMIAL_VEC: \
+ case RAVIART_THOMAS: \
libmesh_error_msg("Error: Can only request scalar valued elements for Real FEInterface::func_and_args"); \
default: \
libmesh_error_msg("Unsupported family = " << Utility::enum_to_string(fe_t.family)); \
@@ -221,6 +224,8 @@ FEInterface::is_InfFE_elem(const ElemType et)
prefix FENedelecOne::func_and_args suffix \
case MONOMIAL_VEC: \
prefix FEMonomialVec::func_and_args suffix \
+ case RAVIART_THOMAS: \
+ prefix FERaviartThomas::func_and_args suffix \
case HERMITE: \
case HIERARCHIC: \
case L2_HIERARCHIC: \
@@ -306,6 +311,8 @@ FEInterface::is_InfFE_elem(const ElemType et)
prefix FE<2,SUBDIVISION>::func_and_args suffix \
case NEDELEC_ONE: \
prefix FENedelecOne::func_and_args suffix \
+ case RAVIART_THOMAS: \
+ prefix FERaviartThomas::func_and_args suffix \
default: \
libmesh_error_msg("Unsupported family = " << Utility::enum_to_string(fe_t.family)); \
} \
@@ -341,6 +348,7 @@ FEInterface::is_InfFE_elem(const ElemType et)
case LAGRANGE_VEC: \
case NEDELEC_ONE: \
case MONOMIAL_VEC: \
+ case RAVIART_THOMAS: \
libmesh_error_msg("Error: Can only request scalar valued elements for Real FEInterface::func_and_args"); \
default: \
libmesh_error_msg("Unsupported family = " << Utility::enum_to_string(fe_t.family)); \
@@ -358,6 +366,8 @@ FEInterface::is_InfFE_elem(const ElemType et)
prefix FENedelecOne::func_and_args suffix \
case MONOMIAL_VEC: \
prefix FEMonomialVec::func_and_args suffix \
+ case RAVIART_THOMAS: \
+ prefix FERaviartThomas::func_and_args suffix \
case HERMITE: \
case HIERARCHIC: \
case L2_HIERARCHIC: \
@@ -2767,6 +2777,20 @@ unsigned int FEInterface::max_order(const FEType & fe_t,
return 0;
}
break;
+ case RAVIART_THOMAS:
+ switch (el_t)
+ {
+ case TRI6:
+ case TRI7:
+ case QUAD8:
+ case QUAD9:
+ case TET14:
+ case HEX27:
+ return 1;
+ default:
+ return 0;
+ }
+ break;
default:
return 0;
break;
@@ -2789,6 +2813,7 @@ bool FEInterface::extra_hanging_dofs(const FEType & fe_t)
case SUBDIVISION:
case LAGRANGE_VEC:
case NEDELEC_ONE:
+ case RAVIART_THOMAS:
return false;
case CLOUGH:
case HERMITE:
@@ -2815,6 +2840,7 @@ FEFieldType FEInterface::field_type (const FEFamily & fe_family)
case LAGRANGE_VEC:
case NEDELEC_ONE:
case MONOMIAL_VEC:
+ case RAVIART_THOMAS:
return TYPE_VECTOR;
default:
return TYPE_SCALAR;
@@ -2831,6 +2857,7 @@ unsigned int FEInterface::n_vec_dim (const MeshBase & mesh,
case LAGRANGE_VEC:
case NEDELEC_ONE:
case MONOMIAL_VEC:
+ case RAVIART_THOMAS:
return mesh.mesh_dimension();
default:
return 1;
@@ -2874,6 +2901,9 @@ FEContinuity FEInterface::get_continuity(const FEType & fe_type)
case NEDELEC_ONE:
return H_CURL;
+ case RAVIART_THOMAS:
+ return H_DIV;
+
// Side elements
case SIDE_HIERARCHIC:
return SIDE_DISCONTINUOUS;
diff --git a/src/fe/fe_raviart.C b/src/fe/fe_raviart.C
new file mode 100644
index 00000000000..08bfe0b530d
--- /dev/null
+++ b/src/fe/fe_raviart.C
@@ -0,0 +1,535 @@
+// The libMesh Finite Element Library.
+// Copyright (C) 2002-2023 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
+
+// This library is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+// Lesser General Public License for more details.
+
+// You should have received a copy of the GNU Lesser General Public
+// License along with this library; if not, write to the Free Software
+// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+
+
+
+// Local includes
+#include "libmesh/dof_map.h"
+#include "libmesh/elem.h"
+#include "libmesh/enum_to_string.h"
+#include "libmesh/fe.h"
+#include "libmesh/fe_interface.h"
+#include "libmesh/fe_macro.h"
+#include "libmesh/tensor_value.h"
+
+
+namespace libMesh
+{
+
+
+LIBMESH_DEFAULT_VECTORIZED_FE(0,RAVIART_THOMAS)
+LIBMESH_DEFAULT_VECTORIZED_FE(1,RAVIART_THOMAS)
+LIBMESH_DEFAULT_VECTORIZED_FE(2,RAVIART_THOMAS)
+LIBMESH_DEFAULT_VECTORIZED_FE(3,RAVIART_THOMAS)
+
+
+// Anonymous namespace for local helper functions
+namespace {
+void raviart_thomas_nodal_soln(const Elem * elem,
+ const Order order,
+ const std::vector & elem_soln,
+ const int dim,
+ std::vector & nodal_soln)
+{
+ const unsigned int n_nodes = elem->n_nodes();
+ const ElemType elem_type = elem->type();
+
+ const Order totalorder = static_cast(order + elem->p_level());
+
+ nodal_soln.resize(n_nodes*dim);
+
+ FEType fe_type(order, RAVIART_THOMAS);
+ FEType p_refined_fe_type(totalorder, RAVIART_THOMAS);
+
+ switch (totalorder)
+ {
+ case FIRST:
+ {
+ switch (elem_type)
+ {
+ case TRI6:
+ case TRI7:
+ {
+ libmesh_assert_equal_to (elem_soln.size(), 3);
+
+ if (elem_type == TRI6)
+ libmesh_assert_equal_to (nodal_soln.size(), 6*2);
+ else
+ libmesh_assert_equal_to (nodal_soln.size(), 7*2);
+ break;
+ }
+ case QUAD8:
+ case QUAD9:
+ {
+ libmesh_assert_equal_to (elem_soln.size(), 4);
+
+ if (elem_type == QUAD8)
+ libmesh_assert_equal_to (nodal_soln.size(), 8*2);
+ else
+ libmesh_assert_equal_to (nodal_soln.size(), 9*2);
+ break;
+ }
+ case TET14:
+ {
+ libmesh_assert_equal_to (elem_soln.size(), 4);
+ libmesh_assert_equal_to (nodal_soln.size(), 14*3);
+ break;
+ }
+ case HEX27:
+ {
+ libmesh_assert_equal_to (elem_soln.size(), 6);
+ libmesh_assert_equal_to (nodal_soln.size(), 27*3);
+ break;
+ }
+
+ default:
+ libmesh_error_msg("ERROR: Invalid ElemType " << Utility::enum_to_string(elem_type) << " selected for RAVIART_THOMAS FE family!");
+
+ } // switch(elem_type)
+
+ const unsigned int n_sf =
+ FEInterface::n_shape_functions(fe_type, elem);
+
+ std::vector refspace_nodes;
+ FEVectorBase::get_refspace_nodes(elem_type,refspace_nodes);
+ libmesh_assert_equal_to (refspace_nodes.size(), n_nodes);
+
+
+ // Need to create new fe object so the shape function has the FETransformation
+ // applied to it.
+ std::unique_ptr vis_fe = FEVectorBase::build(dim, p_refined_fe_type);
+
+ const std::vector> & vis_phi = vis_fe->get_phi();
+
+ vis_fe->reinit(elem,&refspace_nodes);
+
+ for (unsigned int n = 0; n < n_nodes; n++)
+ {
+ libmesh_assert_equal_to (elem_soln.size(), n_sf);
+
+ // Zero before summation
+ for (int d = 0; d < dim; d++)
+ {
+ nodal_soln[dim*n+d] = 0;
+ }
+
+ // u = Sum (u_i phi_i)
+ for (unsigned int i=0; i
+void FE<0,RAVIART_THOMAS>::nodal_soln(const Elem *,
+ const Order,
+ const std::vector &,
+ std::vector &)
+{ RAVIART_LOW_D_ERROR_MESSAGE }
+
+template <>
+void FE<1,RAVIART_THOMAS>::nodal_soln(const Elem *,
+ const Order,
+ const std::vector &,
+ std::vector &)
+{ RAVIART_LOW_D_ERROR_MESSAGE }
+
+template <>
+void FE<2,RAVIART_THOMAS>::nodal_soln(const Elem * elem,
+ const Order order,
+ const std::vector & elem_soln,
+ std::vector & nodal_soln)
+{ raviart_thomas_nodal_soln(elem, order, elem_soln, 2 /*dim*/, nodal_soln); }
+
+template <>
+void FE<3,RAVIART_THOMAS>::nodal_soln(const Elem * elem,
+ const Order order,
+ const std::vector & elem_soln,
+ std::vector & nodal_soln)
+{ raviart_thomas_nodal_soln(elem, order, elem_soln, 3 /*dim*/, nodal_soln); }
+
+LIBMESH_FE_SIDE_NODAL_SOLN(RAVIART_THOMAS)
+
+
+// Do full-specialization for every dimension, instead
+// of explicit instantiation at the end of this function.
+// This could be macro-ified.
+template <> unsigned int FE<0,RAVIART_THOMAS>::n_dofs(const ElemType, const Order) { RAVIART_LOW_D_ERROR_MESSAGE }
+template <> unsigned int FE<1,RAVIART_THOMAS>::n_dofs(const ElemType, const Order) { RAVIART_LOW_D_ERROR_MESSAGE }
+template <> unsigned int FE<2,RAVIART_THOMAS>::n_dofs(const ElemType t, const Order o) { return raviart_thomas_n_dofs(t, o); }
+template <> unsigned int FE<3,RAVIART_THOMAS>::n_dofs(const ElemType t, const Order o) { return raviart_thomas_n_dofs(t, o); }
+
+
+// Do full-specialization for every dimension, instead
+// of explicit instantiation at the end of this function.
+template <> unsigned int FE<0,RAVIART_THOMAS>::n_dofs_at_node(const ElemType, const Order, const unsigned int) { RAVIART_LOW_D_ERROR_MESSAGE }
+template <> unsigned int FE<1,RAVIART_THOMAS>::n_dofs_at_node(const ElemType, const Order, const unsigned int) { RAVIART_LOW_D_ERROR_MESSAGE }
+template <> unsigned int FE<2,RAVIART_THOMAS>::n_dofs_at_node(const ElemType t, const Order o, const unsigned int n) { return raviart_thomas_n_dofs_at_node(t, o, n); }
+template <> unsigned int FE<3,RAVIART_THOMAS>::n_dofs_at_node(const ElemType t, const Order o, const unsigned int n) { return raviart_thomas_n_dofs_at_node(t, o, n); }
+
+
+// Raviart-Thomas elements have no dofs per element
+template <> unsigned int FE<0,RAVIART_THOMAS>::n_dofs_per_elem(const ElemType, const Order) { RAVIART_LOW_D_ERROR_MESSAGE }
+template <> unsigned int FE<1,RAVIART_THOMAS>::n_dofs_per_elem(const ElemType, const Order) { RAVIART_LOW_D_ERROR_MESSAGE }
+template <> unsigned int FE<2,RAVIART_THOMAS>::n_dofs_per_elem(const ElemType, const Order) { return 0; }
+template <> unsigned int FE<3,RAVIART_THOMAS>::n_dofs_per_elem(const ElemType, const Order) { return 0; }
+
+// Raviart-Thomas FEMs are always normally continuous
+template <> FEContinuity FE<0,RAVIART_THOMAS>::get_continuity() const { RAVIART_LOW_D_ERROR_MESSAGE }
+template <> FEContinuity FE<1,RAVIART_THOMAS>::get_continuity() const { RAVIART_LOW_D_ERROR_MESSAGE }
+template <> FEContinuity FE<2,RAVIART_THOMAS>::get_continuity() const { return H_DIV; }
+template <> FEContinuity FE<3,RAVIART_THOMAS>::get_continuity() const { return H_DIV; }
+
+// Raviart-Thomas FEMs are not hierarchic
+template <> bool FE<0,RAVIART_THOMAS>::is_hierarchic() const { RAVIART_LOW_D_ERROR_MESSAGE }
+template <> bool FE<1,RAVIART_THOMAS>::is_hierarchic() const { RAVIART_LOW_D_ERROR_MESSAGE }
+template <> bool FE<2,RAVIART_THOMAS>::is_hierarchic() const { return false; }
+template <> bool FE<3,RAVIART_THOMAS>::is_hierarchic() const { return false; }
+
+// Raviart-Thomas FEM shapes always need to be reinit'ed (because of orientation dependence)
+template <> bool FE<0,RAVIART_THOMAS>::shapes_need_reinit() const { RAVIART_LOW_D_ERROR_MESSAGE }
+template <> bool FE<1,RAVIART_THOMAS>::shapes_need_reinit() const { RAVIART_LOW_D_ERROR_MESSAGE }
+template <> bool FE<2,RAVIART_THOMAS>::shapes_need_reinit() const { return true; }
+template <> bool FE<3,RAVIART_THOMAS>::shapes_need_reinit() const { return true; }
+
+#ifdef LIBMESH_ENABLE_AMR
+template <>
+void FE<0,RAVIART_THOMAS>::compute_constraints (DofConstraints &,
+ DofMap &,
+ const unsigned int,
+ const Elem *)
+{ RAVIART_LOW_D_ERROR_MESSAGE }
+
+template <>
+void FE<1,RAVIART_THOMAS>::compute_constraints (DofConstraints &,
+ DofMap &,
+ const unsigned int,
+ const Elem *)
+{ RAVIART_LOW_D_ERROR_MESSAGE }
+
+template <>
+void FE<2,RAVIART_THOMAS>::compute_constraints (DofConstraints & constraints,
+ DofMap & dof_map,
+ const unsigned int variable_number,
+ const Elem * elem)
+{ raviart_thomas_compute_constraints(constraints, dof_map, variable_number, elem, /*Dim=*/2); }
+
+template <>
+void FE<3,RAVIART_THOMAS>::compute_constraints (DofConstraints & constraints,
+ DofMap & dof_map,
+ const unsigned int variable_number,
+ const Elem * elem)
+{ raviart_thomas_compute_constraints(constraints, dof_map, variable_number, elem, /*Dim=*/3); }
+#endif // LIBMESH_ENABLE_AMR
+
+// Specialize useless shape function methods
+template <>
+RealGradient FE<0,RAVIART_THOMAS>::shape(const ElemType, const Order,const unsigned int,const Point &)
+{ RAVIART_LOW_D_ERROR_MESSAGE }
+template <>
+RealGradient FE<0,RAVIART_THOMAS>::shape(const Elem *,const Order,const unsigned int,const Point &,const bool)
+{ RAVIART_LOW_D_ERROR_MESSAGE }
+template <>
+RealGradient FE<0,RAVIART_THOMAS>::shape_deriv(const ElemType, const Order,const unsigned int,
+ const unsigned int,const Point &)
+{ RAVIART_LOW_D_ERROR_MESSAGE }
+template <>
+RealGradient FE<0,RAVIART_THOMAS>::shape_deriv(const Elem *,const Order,const unsigned int,
+ const unsigned int,const Point &,const bool)
+{ RAVIART_LOW_D_ERROR_MESSAGE }
+
+#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
+template <>
+RealGradient FE<0,RAVIART_THOMAS>::shape_second_deriv(const ElemType, const Order,const unsigned int,
+ const unsigned int,const Point &)
+{ RAVIART_LOW_D_ERROR_MESSAGE }
+template <>
+RealGradient FE<0,RAVIART_THOMAS>::shape_second_deriv(const Elem *,const Order,const unsigned int,
+ const unsigned int,const Point &,const bool)
+{ RAVIART_LOW_D_ERROR_MESSAGE }
+
+#endif
+
+template <>
+RealGradient FE<1,RAVIART_THOMAS>::shape(const ElemType, const Order,const unsigned int,const Point &)
+{ RAVIART_LOW_D_ERROR_MESSAGE }
+template <>
+RealGradient FE<1,RAVIART_THOMAS>::shape(const Elem *,const Order,const unsigned int,const Point &,const bool)
+{ RAVIART_LOW_D_ERROR_MESSAGE }
+template <>
+RealGradient FE<1,RAVIART_THOMAS>::shape_deriv(const ElemType, const Order,const unsigned int,
+ const unsigned int,const Point &)
+{ RAVIART_LOW_D_ERROR_MESSAGE }
+template <>
+RealGradient FE<1,RAVIART_THOMAS>::shape_deriv(const Elem *,const Order,const unsigned int,
+ const unsigned int,const Point &,const bool)
+{ RAVIART_LOW_D_ERROR_MESSAGE }
+
+#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
+template <>
+RealGradient FE<1,RAVIART_THOMAS>::shape_second_deriv(const ElemType, const Order,const unsigned int,
+ const unsigned int,const Point &)
+{ RAVIART_LOW_D_ERROR_MESSAGE }
+template <>
+RealGradient FE<1,RAVIART_THOMAS>::shape_second_deriv(const Elem *,const Order,const unsigned int,
+ const unsigned int,const Point &,const bool)
+{ RAVIART_LOW_D_ERROR_MESSAGE }
+
+#endif
+
+} // namespace libMesh
diff --git a/src/fe/fe_raviart_shape_2D.C b/src/fe/fe_raviart_shape_2D.C
new file mode 100644
index 00000000000..830c449d0d0
--- /dev/null
+++ b/src/fe/fe_raviart_shape_2D.C
@@ -0,0 +1,447 @@
+// The libMesh Finite Element Library.
+// Copyright (C) 2002-2023 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
+
+// This library is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+// Lesser General Public License for more details.
+
+// You should have received a copy of the GNU Lesser General Public
+// License along with this library; if not, write to the Free Software
+// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+
+
+// Local includes
+#include "libmesh/fe.h"
+#include "libmesh/elem.h"
+#include "libmesh/enum_to_string.h"
+
+namespace libMesh
+{
+
+template <>
+RealGradient FE<2,RAVIART_THOMAS>::shape(const Elem * elem,
+ const Order order,
+ const unsigned int i,
+ const Point & p,
+ const bool add_p_level)
+{
+#if LIBMESH_DIM > 1
+ libmesh_assert(elem);
+
+ const Order total_order = static_cast(order + add_p_level * elem->p_level());
+
+ switch (total_order)
+ {
+ // linear Raviart-Thomas shape functions
+ case FIRST:
+ {
+ switch (elem->type())
+ {
+ case QUAD8:
+ case QUAD9:
+ {
+ libmesh_assert_less (i, 4);
+
+ const Real xi = p(0);
+ const Real eta = p(1);
+
+ // Even with a loose inverse_map tolerance we ought to
+ // be nearly on the element interior in master
+ // coordinates
+ libmesh_assert_less_equal ( std::fabs(xi), 1.0+10*TOLERANCE );
+ libmesh_assert_less_equal ( std::fabs(eta), 1.0+10*TOLERANCE );
+
+ switch(i)
+ {
+ case 0:
+ {
+ if (elem->point(0) > elem->point(1))
+ return RealGradient( 0.0, -0.25*(1.0-eta) );
+ else
+ return RealGradient( 0.0, 0.25*(1.0-eta) );
+ }
+ case 1:
+ {
+ if (elem->point(1) > elem->point(2))
+ return RealGradient( 0.25*(1.0+xi), 0.0 );
+ else
+ return RealGradient( -0.25*(1.0+xi), 0.0 );
+ }
+
+ case 2:
+ {
+ if (elem->point(2) > elem->point(3))
+ return RealGradient( 0.0, 0.25*(1.0+eta) );
+ else
+ return RealGradient( 0.0, -0.25*(1.0+eta) );
+ }
+ case 3:
+ {
+ if (elem->point(3) > elem->point(0))
+ return RealGradient( 0.25*(xi-1.0), 0.0 );
+ else
+ return RealGradient( -0.25*(xi-1.0), 0.0 );
+ }
+
+ default:
+ libmesh_error_msg("Invalid i = " << i);
+ }
+
+ return RealGradient();
+ }
+
+ case TRI6:
+ case TRI7:
+ {
+ const Real xi = p(0);
+ const Real eta = p(1);
+
+ libmesh_assert_less (i, 3);
+
+ switch(i)
+ {
+ case 0:
+ {
+ if (elem->point(0) > elem->point(1))
+ return RealGradient( xi, eta-1.0 );
+ else
+ return RealGradient( -xi, -eta+1.0 );
+ }
+ case 1:
+ {
+ if (elem->point(1) > elem->point(2))
+ return RealGradient( xi, eta );
+ else
+ return RealGradient( -xi, -eta );
+ }
+
+ case 2:
+ {
+ if (elem->point(2) > elem->point(0))
+ return RealGradient( xi-1.0, eta );
+ else
+ return RealGradient( -xi+1.0, -eta );
+ }
+
+ default:
+ libmesh_error_msg("Invalid i = " << i);
+ }
+ }
+
+ default:
+ libmesh_error_msg("ERROR: Unsupported 2D element type!: " << Utility::enum_to_string(elem->type()));
+ }
+ }
+
+ // unsupported order
+ default:
+ libmesh_error_msg("ERROR: Unsupported 2D FE order!: " << total_order);
+ }
+#else // LIBMESH_DIM > 1
+ libmesh_ignore(elem, order, i, p, add_p_level);
+ libmesh_not_implemented();
+#endif
+}
+
+
+
+
+template <>
+RealGradient FE<2,RAVIART_THOMAS>::shape(const ElemType,
+ const Order,
+ const unsigned int,
+ const Point &)
+{
+ libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause edge orientation is needed.");
+ return RealGradient();
+}
+
+
+template <>
+RealGradient FE<2,RAVIART_THOMAS>::shape(const FEType fet,
+ const Elem * elem,
+ const unsigned int i,
+ const Point & p,
+ const bool add_p_level)
+{
+ return FE<2,RAVIART_THOMAS>::shape(elem, fet.order, i, p, add_p_level);
+}
+
+template <>
+RealGradient FE<2,RAVIART_THOMAS>::shape_deriv(const Elem * elem,
+ const Order order,
+ const unsigned int i,
+ const unsigned int j,
+ const Point &,
+ const bool add_p_level)
+{
+#if LIBMESH_DIM > 1
+ libmesh_assert(elem);
+ libmesh_assert_less (j, 2);
+
+ const Order total_order = static_cast(order + add_p_level * elem->p_level());
+
+ switch (total_order)
+ {
+ // linear Raviart-Thomas shape function first derivatives
+ case FIRST:
+ {
+ switch (elem->type())
+ {
+ case QUAD8:
+ case QUAD9:
+ {
+ libmesh_assert_less (i, 4);
+
+ switch (j)
+ {
+ // d()/dxi
+ case 0:
+ {
+ switch(i)
+ {
+ case 0:
+ case 2:
+ return RealGradient();
+ case 1:
+ {
+ if (elem->point(1) > elem->point(2))
+ return RealGradient( 0.25 );
+ else
+ return RealGradient( -0.25 );
+ }
+ case 3:
+ {
+ if (elem->point(3) > elem->point(0))
+ return RealGradient( 0.25 );
+ else
+ return RealGradient( -0.25 );
+ }
+ default:
+ libmesh_error_msg("Invalid i = " << i);
+ }
+ } // j = 0
+
+ // d()/deta
+ case 1:
+ {
+ switch(i)
+ {
+ case 1:
+ case 3:
+ return RealGradient();
+ case 0:
+ {
+ if (elem->point(0) > elem->point(1))
+ return RealGradient( 0.0, 0.25 );
+ else
+ return RealGradient( 0.0, -0.25 );
+ }
+ case 2:
+ {
+ if (elem->point(2) > elem->point(3))
+ return RealGradient( 0.0, 0.25 );
+ else
+ return RealGradient( 0.0, -0.25 );
+ }
+ default:
+ libmesh_error_msg("Invalid i = " << i);
+ }
+ } // j = 1
+
+ default:
+ libmesh_error_msg("Invalid j = " << j);
+ }
+
+ return RealGradient();
+ }
+
+ case TRI6:
+ case TRI7:
+ {
+ libmesh_assert_less (i, 3);
+
+ // Account for edge flipping
+ Real f = 1.0;
+
+ switch(i)
+ {
+ case 0:
+ {
+ if (elem->point(0) > elem->point(1))
+ f = -1.0;
+ break;
+ }
+ case 1:
+ {
+ if (elem->point(1) > elem->point(2))
+ f = -1.0;
+ break;
+ }
+ case 2:
+ {
+ if (elem->point(2) > elem->point(0))
+ f = -1.0;
+ break;
+ }
+ default:
+ libmesh_error_msg("Invalid i = " << i);
+ }
+
+ switch (j)
+ {
+ // d()/dxi
+ case 0:
+ {
+ return RealGradient( f*(-1.0) );
+ }
+ // d()/deta
+ case 1:
+ {
+ return RealGradient( 0.0, f*(-1.0) );
+ }
+ default:
+ libmesh_error_msg("Invalid j = " << j);
+ }
+ }
+
+ default:
+ libmesh_error_msg("ERROR: Unsupported 2D element type!: " << Utility::enum_to_string(elem->type()));
+ }
+ }
+ // unsupported order
+ default:
+ libmesh_error_msg("ERROR: Unsupported 2D FE order!: " << total_order);
+ }
+#else // LIBMESH_DIM > 1
+ libmesh_ignore(elem, order, i, j, add_p_level);
+ libmesh_not_implemented();
+#endif
+}
+
+
+
+template <>
+RealGradient FE<2,RAVIART_THOMAS>::shape_deriv(const ElemType,
+ const Order,
+ const unsigned int,
+ const unsigned int,
+ const Point &)
+{
+ libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause edge orientation is needed.");
+ return RealGradient();
+}
+
+template <>
+RealGradient FE<2,RAVIART_THOMAS>::shape_deriv(const FEType fet,
+ const Elem * elem,
+ const unsigned int i,
+ const unsigned int j,
+ const Point & p,
+ const bool add_p_level)
+{
+ return FE<2,RAVIART_THOMAS>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
+}
+
+
+
+
+
+#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
+
+template <>
+RealGradient FE<2,RAVIART_THOMAS>::shape_second_deriv(const Elem * elem,
+ const Order order,
+ const unsigned int libmesh_dbg_var(i),
+ const unsigned int libmesh_dbg_var(j),
+ const Point &,
+ const bool add_p_level)
+{
+#if LIBMESH_DIM > 1
+ libmesh_assert(elem);
+
+ // j = 0 ==> d^2 phi / dxi^2
+ // j = 1 ==> d^2 phi / dxi deta
+ // j = 2 ==> d^2 phi / deta^2
+ libmesh_assert_less (j, 3);
+
+ const Order total_order = static_cast(order + add_p_level * elem->p_level());
+
+ switch (total_order)
+ {
+ // linear Raviart-Thomas shape function second derivatives
+ case FIRST:
+ {
+ switch (elem->type())
+ {
+ case QUAD8:
+ case QUAD9:
+ {
+ libmesh_assert_less (i, 4);
+ // All second derivatives for linear quads are zero.
+ return RealGradient();
+ }
+
+ case TRI6:
+ case TRI7:
+ {
+ libmesh_assert_less (i, 3);
+ // All second derivatives for linear triangles are zero.
+ return RealGradient();
+ }
+
+ default:
+ libmesh_error_msg("ERROR: Unsupported 2D element type!: " << Utility::enum_to_string(elem->type()));
+
+ } // end switch (type)
+ } // end case FIRST
+
+ // unsupported order
+ default:
+ libmesh_error_msg("ERROR: Unsupported 2D FE order!: " << total_order);
+
+ } // end switch (order)
+
+#else // LIBMESH_DIM > 1
+ libmesh_assert(true || i || j);
+ libmesh_ignore(elem, order, add_p_level);
+ libmesh_not_implemented();
+#endif
+}
+
+
+
+template <>
+RealGradient FE<2,RAVIART_THOMAS>::shape_second_deriv(const ElemType,
+ const Order,
+ const unsigned int,
+ const unsigned int,
+ const Point &)
+{
+ libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause edge orientation is needed.");
+ return RealGradient();
+}
+
+
+template <>
+RealGradient FE<2,RAVIART_THOMAS>::shape_second_deriv(const FEType fet,
+ const Elem * elem,
+ const unsigned int i,
+ const unsigned int j,
+ const Point & p,
+ const bool add_p_level)
+{
+ return FE<2,RAVIART_THOMAS>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
+}
+
+
+
+#endif
+
+} // namespace libMesh
diff --git a/src/fe/fe_raviart_shape_3D.C b/src/fe/fe_raviart_shape_3D.C
new file mode 100644
index 00000000000..e75f8562047
--- /dev/null
+++ b/src/fe/fe_raviart_shape_3D.C
@@ -0,0 +1,629 @@
+// The libMesh Finite Element Library.
+// Copyright (C) 2002-2023 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
+
+// This library is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+// Lesser General Public License for more details.
+
+// You should have received a copy of the GNU Lesser General Public
+// License along with this library; if not, write to the Free Software
+// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+
+
+// Local includes
+#include "libmesh/fe.h"
+#include "libmesh/elem.h"
+#include "libmesh/enum_to_string.h"
+
+namespace libMesh
+{
+
+
+bool orientation(std::vector & arr)
+{
+ while (std::min_element(arr.begin(), arr.end()) != arr.begin())
+ std::rotate(arr.begin(), arr.begin() + 1, arr.end());
+
+ size_t cnt = 0;
+ for(size_t i = 0; i < arr.size(); i++)
+ for(size_t j = i + 1; j < arr.size(); j++)
+ if (arr[i] > arr[j]) cnt++;
+ return cnt % 2;
+}
+
+
+template <>
+RealGradient FE<3,RAVIART_THOMAS>::shape(const Elem * elem,
+ const Order order,
+ const unsigned int i,
+ const Point & p,
+ const bool add_p_level)
+{
+#if LIBMESH_DIM == 3
+ libmesh_assert(elem);
+
+ const Order totalorder = static_cast(order + add_p_level * elem->p_level());
+
+ switch (totalorder)
+ {
+ // linear Raviart-Thomas shape functions
+ case FIRST:
+ {
+ switch (elem->type())
+ {
+ case HEX27:
+ {
+ libmesh_assert_less (i, 6);
+
+ const Real xi = p(0);
+ const Real eta = p(1);
+ const Real zeta = p(2);
+
+ // Even with a loose inverse_map tolerance we ought to
+ // be nearly on the element interior in master
+ // coordinates
+ libmesh_assert_less_equal ( std::fabs(xi), 1.0+10*TOLERANCE );
+ libmesh_assert_less_equal ( std::fabs(eta), 1.0+10*TOLERANCE );
+ libmesh_assert_less_equal ( std::fabs(zeta), 1.0+10*TOLERANCE );
+
+ switch(i)
+ {
+ case 0:
+ {
+ std::vector arr = {elem->point(1), elem->point(0), elem->point(3), elem->point(2)};
+ if (orientation(arr))
+ return RealGradient( 0.0, 0.0, 0.125*(zeta-1.0) );
+ else
+ return RealGradient( 0.0, 0.0, -0.125*(zeta-1.0) );
+ }
+ case 1:
+ {
+ std::vector arr = {elem->point(4), elem->point(0), elem->point(1), elem->point(5)};
+ if (orientation(arr))
+ return RealGradient( 0.0, 0.125*(eta-1.0), 0.0 );
+ else
+ return RealGradient( 0.0, -0.125*(eta-1.0), 0.0 );
+ }
+ case 2:
+ {
+ std::vector arr = {elem->point(6), elem->point(5), elem->point(1), elem->point(2)};
+ if (orientation(arr))
+ return RealGradient( 0.125*(xi+1.0), 0.0, 0.0 );
+ else
+ return RealGradient( -0.125*(xi+1.0), 0.0, 0.0 );
+ }
+ case 3:
+ {
+ std::vector arr = {elem->point(7), elem->point(6), elem->point(2), elem->point(3)};
+ if (orientation(arr))
+ return RealGradient( 0.0, 0.125*(1.0+eta), 0.0 );
+ else
+ return RealGradient( 0.0, -0.125*(1.0+eta), 0.0 );
+ }
+ case 4:
+ {
+ std::vector arr = {elem->point(7), elem->point(3), elem->point(0), elem->point(4)};
+ if (orientation(arr))
+ return RealGradient( 0.125*(xi-1.0), 0.0, 0.0 );
+ else
+ return RealGradient( -0.125*(xi-1.0), 0.0, 0.0 );
+ }
+ case 5:
+ {
+ std::vector arr = {elem->point(5), elem->point(6), elem->point(7), elem->point(4)};
+ if (orientation(arr))
+ return RealGradient( 0.0, 0.0, 0.125*(1.0+zeta) );
+ else
+ return RealGradient( 0.0, 0.0, -0.125*(1.0+zeta) );
+ }
+ default:
+ libmesh_error_msg("Invalid i = " << i);
+ }
+
+ return RealGradient();
+ }
+
+ case TET14:
+ {
+ libmesh_assert_less (i, 4);
+
+ const Real xi = p(0);
+ const Real eta = p(1);
+ const Real zeta = p(2);
+
+ switch(i)
+ {
+ case 0:
+ {
+ std::vector arr = {elem->point(0), elem->point(2), elem->point(1)};
+ if (orientation(arr))
+ return RealGradient( 2.0*xi, 2.0*eta, 2.0*zeta-2.0 );
+ else
+ return RealGradient( -2.0*xi, -2.0*eta, -2.0*zeta+2.0 );
+ }
+ case 1:
+ {
+ std::vector arr = {elem->point(1), elem->point(3), elem->point(0)};
+ if (orientation(arr))
+ return RealGradient( 2.0*xi, 2.0*eta-2.0, 2.0*zeta );
+ else
+ return RealGradient( -2.0*xi, -2.0*eta+2.0, -2.0*zeta );
+ }
+ case 2:
+ {
+ std::vector arr = {elem->point(1), elem->point(2), elem->point(3)};
+ if (orientation(arr))
+ return RealGradient( 2.0*xi, 2.0*eta, 2.0*zeta );
+ else
+ return RealGradient( -2.0*xi, -2.0*eta, -2.0*zeta );
+ }
+ case 3:
+ {
+ std::vector arr = {elem->point(0), elem->point(3), elem->point(2)};
+ if (orientation(arr))
+ return RealGradient( 2.0*xi-2.0, 2.0*eta, 2.0*zeta );
+ else
+ return RealGradient( -2.0*xi+2.0, -2.0*eta, -2.0*zeta );
+ }
+ default:
+ libmesh_error_msg("Invalid i = " << i);
+ }
+
+ return RealGradient();
+ }
+
+ default:
+ libmesh_error_msg("ERROR: Unsupported 3D element type!: " << Utility::enum_to_string(elem->type()));
+ }
+ }
+
+ // unsupported order
+ default:
+ libmesh_error_msg("ERROR: Unsupported 3D FE order!: " << totalorder);
+ }
+#else // LIBMESH_DIM != 3
+ libmesh_ignore(elem, order, i, p, add_p_level);
+ libmesh_not_implemented();
+#endif
+}
+
+
+
+template <>
+RealGradient FE<3,RAVIART_THOMAS>::shape(const ElemType,
+ const Order,
+ const unsigned int,
+ const Point &)
+{
+ libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause face orientation is needed.");
+ return RealGradient();
+}
+
+
+
+template <>
+RealGradient FE<3,RAVIART_THOMAS>::shape(const FEType fet,
+ const Elem * elem,
+ const unsigned int i,
+ const Point & p,
+ const bool add_p_level)
+{
+ return FE<3,RAVIART_THOMAS>::shape(elem, fet.order, i, p, add_p_level);
+}
+
+
+template <>
+RealGradient FE<3,RAVIART_THOMAS>::shape_deriv(const Elem * elem,
+ const Order order,
+ const unsigned int i,
+ const unsigned int j,
+ const Point &,
+ const bool add_p_level)
+{
+#if LIBMESH_DIM == 3
+ libmesh_assert(elem);
+ libmesh_assert_less (j, 3);
+
+ const Order totalorder = static_cast(order + add_p_level * elem->p_level());
+
+ switch (totalorder)
+ {
+ // linear Raviart-Thomas shape function first derivatives
+ case FIRST:
+ {
+ switch (elem->type())
+ {
+ case HEX27:
+ {
+ libmesh_assert_less (i, 6);
+
+ switch (j)
+ {
+ // d()/dxi
+ case 0:
+ {
+ switch(i)
+ {
+ case 0:
+ case 1:
+ case 3:
+ case 5:
+ return RealGradient();
+ case 2:
+ {
+ std::vector arr = {elem->point(6), elem->point(5), elem->point(1), elem->point(2)};
+ if (orientation(arr))
+ return RealGradient( 0.125, 0.0, 0.0 );
+ else
+ return RealGradient( -0.125, 0.0, 0.0 );
+ }
+ case 4:
+ {
+ std::vector arr = {elem->point(7), elem->point(3), elem->point(0), elem->point(4)};
+ if (orientation(arr))
+ return RealGradient( 0.125, 0.0, 0.0 );
+ else
+ return RealGradient( -0.125, 0.0, 0.0 );
+ }
+ default:
+ libmesh_error_msg("Invalid i = " << i);
+ } // switch(i)
+
+ } // j = 0
+
+ // d()/deta
+ case 1:
+ {
+ switch(i)
+ {
+ case 0:
+ case 2:
+ case 4:
+ case 5:
+ return RealGradient();
+ case 1:
+ {
+ std::vector arr = {elem->point(4), elem->point(0), elem->point(1), elem->point(5)};
+ if (orientation(arr))
+ return RealGradient( 0.0, 0.125, 0.0 );
+ else
+ return RealGradient( 0.0, -0.125, 0.0 );
+ }
+ case 3:
+ {
+ std::vector arr = {elem->point(7), elem->point(6), elem->point(2), elem->point(3)};
+ if (orientation(arr))
+ return RealGradient( 0.0, 0.125, 0.0 );
+ else
+ return RealGradient( 0.0, -0.125, 0.0 );
+ }
+ default:
+ libmesh_error_msg("Invalid i = " << i);
+ } // switch(i)
+
+ } // j = 1
+
+ // d()/dzeta
+ case 2:
+ {
+ switch(i)
+ {
+ case 1:
+ case 2:
+ case 3:
+ case 4:
+ return RealGradient();
+ case 0:
+ {
+ std::vector arr = {elem->point(1), elem->point(0), elem->point(3), elem->point(2)};
+ if (orientation(arr))
+ return RealGradient( 0.0, 0.0, 0.125 );
+ else
+ return RealGradient( 0.0, 0.0, -0.125 );
+ }
+ case 5:
+ {
+ std::vector arr = {elem->point(5), elem->point(6), elem->point(7), elem->point(4)};
+ if (orientation(arr))
+ return RealGradient( 0.0, 0.0, 0.125 );
+ else
+ return RealGradient( 0.0, 0.0, -0.125 );
+ }
+ default:
+ libmesh_error_msg("Invalid i = " << i);
+ } // switch(i)
+
+ } // j = 2
+
+ default:
+ libmesh_error_msg("Invalid j = " << j);
+ }
+
+ return RealGradient();
+ }
+
+ case TET14:
+ {
+ libmesh_assert_less (i, 4);
+
+ switch (j)
+ {
+ // d()/dxi
+ case 0:
+ {
+ switch(i)
+ {
+ case 0:
+ {
+ std::vector arr = {elem->point(0), elem->point(2), elem->point(1)};
+ if (orientation(arr))
+ return RealGradient( 2.0, 0.0, 0.0 );
+ else
+ return RealGradient( -2.0, 0.0, 0.0 );
+ }
+ case 1:
+ {
+ std::vector arr = {elem->point(1), elem->point(3), elem->point(0)};
+ if (orientation(arr))
+ return RealGradient( 2.0, 0.0, 0.0 );
+ else
+ return RealGradient( -2.0, 0.0, 0.0 );
+ }
+ case 2:
+ {
+ std::vector arr = {elem->point(1), elem->point(2), elem->point(3)};
+ if (orientation(arr))
+ return RealGradient( 2.0, 0.0, 0.0 );
+ else
+ return RealGradient( -2.0, 0.0, 0.0 );
+ }
+ case 3:
+ {
+ std::vector arr = {elem->point(0), elem->point(3), elem->point(2)};
+ if (orientation(arr))
+ return RealGradient( 2.0, 0.0, 0.0 );
+ else
+ return RealGradient( -2.0, 0.0, 0.0 );
+ }
+ default:
+ libmesh_error_msg("Invalid i = " << i);
+ } // switch(i)
+
+ } // j = 0
+
+ // d()/deta
+ case 1:
+ {
+ switch(i)
+ {
+ case 0:
+ {
+ std::vector arr = {elem->point(0), elem->point(2), elem->point(1)};
+ if (orientation(arr))
+ return RealGradient( 0.0, 2.0, 0.0 );
+ else
+ return RealGradient( 0.0, -2.0, 0.0 );
+ }
+ case 1:
+ {
+ std::vector arr = {elem->point(1), elem->point(3), elem->point(0)};
+ if (orientation(arr))
+ return RealGradient( 0.0, 2.0, 0.0 );
+ else
+ return RealGradient( 0.0, -2.0, 0.0 );
+ }
+ case 2:
+ {
+ std::vector arr = {elem->point(1), elem->point(2), elem->point(3)};
+ if (orientation(arr))
+ return RealGradient( 0.0, 2.0, 0.0 );
+ else
+ return RealGradient( 0.0, -2.0, 0.0 );
+ }
+ case 3:
+ {
+ std::vector arr = {elem->point(0), elem->point(3), elem->point(2)};
+ if (orientation(arr))
+ return RealGradient( 0.0, 2.0, 0.0 );
+ else
+ return RealGradient( 0.0, -2.0, 0.0 );
+ }
+ default:
+ libmesh_error_msg("Invalid i = " << i);
+ } // switch(i)
+
+ } // j = 1
+
+ // d()/dzeta
+ case 2:
+ {
+ switch(i)
+ {
+ case 0:
+ {
+ std::vector arr = {elem->point(0), elem->point(2), elem->point(1)};
+ if (orientation(arr))
+ return RealGradient( 0.0, 0.0, 2.0 );
+ else
+ return RealGradient( 0.0, 0.0, -2.0 );
+ }
+ case 1:
+ {
+ std::vector arr = {elem->point(1), elem->point(3), elem->point(0)};
+ if (orientation(arr))
+ return RealGradient( 0.0, 0.0, 2.0 );
+ else
+ return RealGradient( 0.0, 0.0, -2.0 );
+ }
+ case 2:
+ {
+ std::vector arr = {elem->point(1), elem->point(2), elem->point(3)};
+ if (orientation(arr))
+ return RealGradient( 0.0, 0.0, 2.0 );
+ else
+ return RealGradient( 0.0, 0.0, -2.0 );
+ }
+ case 3:
+ {
+ std::vector arr = {elem->point(0), elem->point(3), elem->point(2)};
+ if (orientation(arr))
+ return RealGradient( 0.0, 0.0, 2.0 );
+ else
+ return RealGradient( 0.0, 0.0, -2.0 );
+ }
+ default:
+ libmesh_error_msg("Invalid i = " << i);
+ } // switch(i)
+
+ } // j = 2
+
+ default:
+ libmesh_error_msg("Invalid j = " << j);
+ }
+
+ return RealGradient();
+ }
+
+ default:
+ libmesh_error_msg("ERROR: Unsupported 3D element type!: " << Utility::enum_to_string(elem->type()));
+ }
+ }
+ // unsupported order
+ default:
+ libmesh_error_msg("ERROR: Unsupported 3D FE order!: " << totalorder);
+ }
+
+#else // LIBMESH_DIM != 3
+ libmesh_ignore(elem, order, i, j, p, add_p_level);
+ libmesh_not_implemented();
+#endif
+}
+
+
+
+
+template <>
+RealGradient FE<3,RAVIART_THOMAS>::shape_deriv(const ElemType,
+ const Order,
+ const unsigned int,
+ const unsigned int,
+ const Point &)
+{
+ libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause face orientation is needed.");
+ return RealGradient();
+}
+
+
+template <>
+RealGradient FE<3,RAVIART_THOMAS>::shape_deriv(const FEType fet,
+ const Elem * elem,
+ const unsigned int i,
+ const unsigned int j,
+ const Point & p,
+ const bool add_p_level)
+{
+ return FE<3,RAVIART_THOMAS>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
+}
+
+
+
+#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
+
+template <>
+RealGradient FE<3,RAVIART_THOMAS>::shape_second_deriv(const Elem * elem,
+ const Order order,
+ const unsigned int libmesh_dbg_var(i),
+ const unsigned int libmesh_dbg_var(j),
+ const Point &,
+ const bool add_p_level)
+{
+#if LIBMESH_DIM == 3
+
+ libmesh_assert(elem);
+
+ // j = 0 ==> d^2 phi / dxi^2
+ // j = 1 ==> d^2 phi / dxi deta
+ // j = 2 ==> d^2 phi / deta^2
+ // j = 3 ==> d^2 phi / dxi dzeta
+ // j = 4 ==> d^2 phi / deta dzeta
+ // j = 5 ==> d^2 phi / dzeta^2
+ libmesh_assert_less (j, 6);
+
+ const Order totalorder = static_cast(order + add_p_level * elem->p_level());
+
+ switch (totalorder)
+ {
+ // linear Raviart-Thomas shape function second derivatives
+ case FIRST:
+ {
+ switch (elem->type())
+ {
+ case HEX27:
+ {
+ libmesh_assert_less (i, 6);
+ // All second derivatives for linear hexes are zero.
+ return RealGradient();
+ }
+
+ case TET14:
+ {
+ libmesh_assert_less (i, 4);
+ // All second derivatives for linear tets are zero.
+ return RealGradient();
+ }
+
+ default:
+ libmesh_error_msg("ERROR: Unsupported 3D element type!: " << Utility::enum_to_string(elem->type()));
+
+ } //switch(type)
+
+ } // case FIRST:
+ // unsupported order
+ default:
+ libmesh_error_msg("ERROR: Unsupported 3D FE order!: " << totalorder);
+ }
+
+#else // LIBMESH_DIM != 3
+ libmesh_assert(true || p(0));
+ libmesh_ignore(elem, order, i, j, add_p_level);
+ libmesh_not_implemented();
+#endif
+}
+
+
+
+template <>
+RealGradient FE<3,RAVIART_THOMAS>::shape_second_deriv(const ElemType,
+ const Order,
+ const unsigned int,
+ const unsigned int,
+ const Point &)
+{
+ libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause face orientation is needed.");
+ return RealGradient();
+}
+
+
+
+template <>
+RealGradient FE<3,RAVIART_THOMAS>::shape_second_deriv(const FEType fet,
+ const Elem * elem,
+ const unsigned int i,
+ const unsigned int j,
+ const Point & p,
+ const bool add_p_level)
+{
+ return FE<3,RAVIART_THOMAS>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
+}
+
+
+
+#endif
+
+} // namespace libMesh
diff --git a/src/fe/fe_transformation_base.C b/src/fe/fe_transformation_base.C
index bc3568e0b3b..fa0fddb702d 100644
--- a/src/fe/fe_transformation_base.C
+++ b/src/fe/fe_transformation_base.C
@@ -18,6 +18,7 @@
#include "libmesh/fe_transformation_base.h"
#include "libmesh/h1_fe_transformation.h"
#include "libmesh/hcurl_fe_transformation.h"
+#include "libmesh/hdiv_fe_transformation.h"
#include "libmesh/fe_type.h"
#include "libmesh/enum_to_string.h"
@@ -57,6 +58,9 @@ std::unique_ptr> FETransformationBase>();
// HDiv Conforming Elements
+ case RAVIART_THOMAS:
+ return std::make_unique>();
+
// L2 Conforming Elements
// Other...
diff --git a/src/fe/hdiv_fe_transformation.C b/src/fe/hdiv_fe_transformation.C
new file mode 100644
index 00000000000..4e1714b657e
--- /dev/null
+++ b/src/fe/hdiv_fe_transformation.C
@@ -0,0 +1,232 @@
+// The libMesh Finite Element Library.
+// Copyright (C) 2002-2023 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
+
+// This library is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+// Lesser General Public License for more details.
+
+// You should have received a copy of the GNU Lesser General Public
+// License along with this library; if not, write to the Free Software
+// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+
+#include "libmesh/hdiv_fe_transformation.h"
+#include "libmesh/fe_interface.h"
+#include "libmesh/int_range.h"
+
+namespace libMesh
+{
+
+template
+void HDivFETransformation::init_map_phi(const FEGenericBase & fe) const
+{
+ fe.get_fe_map().get_dxidx();
+}
+
+
+
+template
+void HDivFETransformation::init_map_dphi(const FEGenericBase & fe) const
+{
+ fe.get_fe_map().get_dxidx();
+}
+
+
+
+template
+void HDivFETransformation::init_map_d2phi(const FEGenericBase & fe) const
+{
+ fe.get_fe_map().get_dxidx();
+#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
+ fe.get_fe_map().get_d2xidxyz2();
+#endif
+}
+
+
+
+template
+void HDivFETransformation::map_phi(const unsigned int dim,
+ const Elem * const elem,
+ const std::vector & qp,
+ const FEGenericBase & fe,
+ std::vector> & phi,
+ const bool /*add_p_level*/) const
+{
+ switch (dim)
+ {
+ case 0:
+ case 1:
+ libmesh_error_msg("These element transformations only make sense in 2D and 3D.");
+
+ case 2:
+ {
+ const std::vector & dxyz_dxi = fe.get_fe_map().get_dxyzdxi();
+ const std::vector & dxyz_deta = fe.get_fe_map().get_dxyzdeta();
+
+ const std::vector & J = fe.get_fe_map().get_jacobian();
+
+ // phi = J^{-1} * (dx/dxi) * \hat{phi}
+ for (auto i : index_range(phi))
+ for (auto p : index_range(phi[i]))
+ {
+ Real dx_dxi = dxyz_dxi[p](0);
+ Real dx_deta = dxyz_deta[p](0);
+
+ Real dy_dxi = dxyz_dxi[p](1);
+ Real dy_deta = dxyz_deta[p](1);
+
+ // Need to temporarily cache reference shape functions
+ // We are computing mapping basis functions, so we explicitly ignore
+ // any non-zero p_level() the Elem might have.
+ OutputShape phi_ref;
+ FEInterface::shape(fe.get_fe_type(), /*extra_order=*/0, elem, i, qp[p], phi_ref);
+
+ phi[i][p](0) = (dx_dxi*phi_ref(0) + dx_deta*phi_ref(1))/J[p];
+ phi[i][p](1) = (dy_dxi*phi_ref(0) + dy_deta*phi_ref(1))/J[p];
+ }
+
+ break;
+ }
+ case 3:
+ {
+ const std::vector & dxyz_dxi = fe.get_fe_map().get_dxyzdxi();
+ const std::vector & dxyz_deta = fe.get_fe_map().get_dxyzdeta();
+ const std::vector & dxyz_dzeta = fe.get_fe_map().get_dxyzdzeta();
+
+ const std::vector & J = fe.get_fe_map().get_jacobian();
+
+ // phi = J^{-1} * (dx/dxi) * \hat{phi}
+ for (auto i : index_range(phi))
+ for (auto p : index_range(phi[i]))
+ {
+ Real dx_dxi = dxyz_dxi[p](0);
+ Real dx_deta = dxyz_deta[p](0);
+ Real dx_dzeta = dxyz_dzeta[p](0);
+
+ Real dy_dxi = dxyz_dxi[p](1);
+ Real dy_deta = dxyz_deta[p](1);
+ Real dy_dzeta = dxyz_dzeta[p](1);
+
+ Real dz_dxi = dxyz_dxi[p](2);
+ Real dz_deta = dxyz_deta[p](2);
+ Real dz_dzeta = dxyz_dzeta[p](2);
+
+ // Need to temporarily cache reference shape functions
+ // We are computing mapping basis functions, so we explicitly ignore
+ // any non-zero p_level() the Elem might have.
+ OutputShape phi_ref;
+ FEInterface::shape(fe.get_fe_type(), /*extra_order=*/0, elem, i, qp[p], phi_ref);
+
+ phi[i][p](0) = (dx_dxi*phi_ref(0) + dx_deta*phi_ref(1) + dx_dzeta*phi_ref(2))/J[p];
+ phi[i][p](1) = (dy_dxi*phi_ref(0) + dy_deta*phi_ref(1) + dy_dzeta*phi_ref(2))/J[p];
+ phi[i][p](2) = (dz_dxi*phi_ref(0) + dz_deta*phi_ref(1) + dz_dzeta*phi_ref(2))/J[p];
+ }
+
+ break;
+ }
+
+ default:
+ libmesh_error_msg("Invalid dim = " << dim);
+ } // switch(dim)
+}
+
+template
+void HDivFETransformation::map_div(const unsigned int dim,
+ const Elem * const,
+ const std::vector &,
+ const FEGenericBase & fe,
+ std::vector::OutputDivergence>> & div_phi) const
+{
+ switch (dim)
+ {
+ case 0:
+ case 1:
+ libmesh_error_msg("These element transformations only make sense in 2D and 3D.");
+
+ case 2:
+ {
+ const std::vector> & dphi_dxi = fe.get_dphidxi();
+ const std::vector> & dphi_deta = fe.get_dphideta();
+
+ const std::vector & J = fe.get_fe_map().get_jacobian();
+
+ // div(phi) = J^{-1} * div(\hat{phi})
+ for (auto i : index_range(div_phi))
+ for (auto p : index_range(div_phi[i]))
+ {
+ div_phi[i][p] = (dphi_dxi[i][p](0) + dphi_deta[i][p](1))/J[p];
+ }
+
+ break;
+ }
+ case 3:
+ {
+ const std::vector> & dphi_dxi = fe.get_dphidxi();
+ const std::vector> & dphi_deta = fe.get_dphideta();
+ const std::vector> & dphi_dzeta = fe.get_dphidzeta();
+
+ const std::vector & J = fe.get_fe_map().get_jacobian();
+
+ // div(phi) = J^{-1} * div(\hat{phi})
+ for (auto i : index_range(div_phi))
+ for (auto p : index_range(div_phi[i]))
+ {
+ div_phi[i][p] = (dphi_dxi[i][p](0) + dphi_deta[i][p](1) + dphi_dzeta[i][p](2))/J[p];
+ }
+
+ break;
+ }
+
+ default:
+ libmesh_error_msg("Invalid dim = " << dim);
+ } // switch(dim)
+}
+
+template class LIBMESH_EXPORT HDivFETransformation;
+
+template<>
+void HDivFETransformation::init_map_phi(const FEGenericBase & ) const
+{
+ libmesh_error_msg("HDiv transformations only make sense for vector-valued elements.");
+}
+
+template<>
+void HDivFETransformation::init_map_dphi(const FEGenericBase & ) const
+{
+ libmesh_error_msg("HDiv transformations only make sense for vector-valued elements.");
+}
+
+template<>
+void HDivFETransformation::init_map_d2phi(const FEGenericBase & ) const
+{
+ libmesh_error_msg("HDiv transformations only make sense for vector-valued elements.");
+}
+
+template<>
+void HDivFETransformation::map_phi(const unsigned int,
+ const Elem * const,
+ const std::vector &,
+ const FEGenericBase &,
+ std::vector> &,
+ bool) const
+{
+ libmesh_error_msg("HDiv transformations only make sense for vector-valued elements.");
+}
+
+template<>
+void HDivFETransformation::map_div(const unsigned int,
+ const Elem * const,
+ const std::vector &,
+ const FEGenericBase &,
+ std::vector> &) const
+{
+ libmesh_error_msg("HDiv transformations only make sense for vector-valued elements.");
+}
+
+
+} // namespace libMesh
diff --git a/src/libmesh_SOURCES b/src/libmesh_SOURCES
index aa6e08b3833..7fd75ceb99c 100644
--- a/src/libmesh_SOURCES
+++ b/src/libmesh_SOURCES
@@ -81,6 +81,9 @@ libmesh_SOURCES = \
src/fe/fe_rational_shape_1D.C \
src/fe/fe_rational_shape_2D.C \
src/fe/fe_rational_shape_3D.C \
+ src/fe/fe_raviart.C \
+ src/fe/fe_raviart_shape_2D.C \
+ src/fe/fe_raviart_shape_3D.C \
src/fe/fe_scalar.C \
src/fe/fe_scalar_shape_0D.C \
src/fe/fe_scalar_shape_1D.C \
@@ -104,6 +107,7 @@ libmesh_SOURCES = \
src/fe/fe_xyz_shape_3D.C \
src/fe/h1_fe_transformation.C \
src/fe/hcurl_fe_transformation.C \
+ src/fe/hdiv_fe_transformation.C \
src/fe/inf_fe.C \
src/fe/inf_fe_base_radial.C \
src/fe/inf_fe_boundary.C \
diff --git a/src/utils/string_to_enum.C b/src/utils/string_to_enum.C
index 24f6a3074a5..293a541dfd9 100644
--- a/src/utils/string_to_enum.C
+++ b/src/utils/string_to_enum.C
@@ -276,6 +276,7 @@ void init_fefamily_to_enum ()
fefamily_to_enum["HERMITE" ]=HERMITE;
fefamily_to_enum["SUBDIVISION" ]=SUBDIVISION;
fefamily_to_enum["NEDELEC_ONE" ]=NEDELEC_ONE;
+ fefamily_to_enum["RAVIART_THOMAS" ]=RAVIART_THOMAS;
}
}