Use FunctionPenaltyDirichletBC in Hermite convergence tests.

* Drop redundant periodic, FunctionNeumannBCs, and associated Functions.
* We have to use FunctionPenaltyDirichletBC with Hermites because
  MOOSE does not correctly handle the setting of DirichletBCs for
  HERMITE elements.
* Switch test to use new [Adaptivity] system. Note that this changes
  this output of the 'dofs' postprocessor since there are now
  elemental dofs for the marker variable in the system. This required
  regolding the tests, but I checked to make sure that the solutions
  were still the same.
* Drop gold files that were not used for anything.
* If you use periodic BCs, you should not apply any other kind of BC
  on that boundary.
* Reduce the order of the custom quadrature rule used. This seemed to
  make no difference in the results and might speed up the test just a
  bit.

Refs idaholab#2190.

test/tests/variables/fe_hermite_convergence/hermite_converge_neumann.i → test/tests/variables/fe_hermite_convergence/hermite_converge_dirichlet.i

@@ -20,24 +20,6 @@
     grad_x = -pi*cos(pi*x)*sin(pi*y)
     grad_y = -pi*sin(pi*x)*cos(pi*y)
   [../]
-
-  [./bc_fnr]
-    type = ParsedFunction
-    value = -pi*cos(pi*x)*sin(pi*y)
-  [../]
-  [./bc_fnl]
-    type = ParsedFunction
-    value = pi*cos(pi*x)*sin(pi*y)
-  [../]
-  [./bc_fnt]
-    type = ParsedFunction
-    value = -pi*sin(pi*x)*cos(pi*y)
-  [../]
-  [./bc_fnb]
-    type = ParsedFunction
-    value = pi*sin(pi*x)*cos(pi*y)
-  [../]
-
   [./forcing_fn]
     type = ParsedFunction
     value = -2*pi*pi*sin(pi*x)*sin(pi*y)-sin(pi*x)*sin(pi*y)
@@ -52,17 +34,14 @@
 []
 
 [Kernels]
-  active = 'diff forcing reaction'
   [./diff]
     type = Diffusion
     variable = u
   [../]
-
   [./reaction]
     type = Reaction
     variable = u
   [../]
-
   [./forcing]
     type = BodyForce
     variable = u
@@ -72,53 +51,22 @@
 
 [BCs]
   [./all]
-    type = FunctionDirichletBC
+    type = FunctionPenaltyDirichletBC
     variable = u
     boundary = 'bottom right top left'
     function = bc_fn
-  [../]
-  [./Periodic]
-    [./all]
-      variable = u
-      auto_direction= 'x y'
-    [../]
-  [../]
-  [./bc_right]
-    type=FunctionNeumannBC
-    variable = u
-    boundary = 'right'
-    function = bc_fnr
-  [../]
-  [./bc_left]
-    type=FunctionNeumannBC
-    variable = u
-    boundary = 'left'
-    function = bc_fnl
-  [../]
-  [./bc_top]
-    type=FunctionNeumannBC
-    variable = u
-    boundary = 'top'
-    function = bc_fnt
-  [../]
-  [./bc_bottom]
-    type=FunctionNeumannBC
-    variable = u
-    boundary = 'bottom'
-    function = bc_fnb
+    penalty = 1e10
   [../]
 []
 
 [Postprocessors]
   [./dofs]
     type = NumDOFs
   [../]
-
   [./h]
     type = AverageElementSize
     variable = u
   [../]
-
   [./L2error]
     type = ElementL2Error
     variable = u
@@ -138,20 +86,27 @@
 
 [Executioner]
   type = Steady
-
   solve_type = 'NEWTON'
 
-  [./Adaptivity]
-    steps = 2
-    refine_fraction = 1
-    coarsen_fraction = 0
-    max_h_level = 10
-  [../]
+  # We use higher-order quadrature to ensure that the forcing function
+  # is integrated accurately.
   [./Quadrature]
-    order=FIFTEENTH
+    order=ELEVENTH
   [../]
 []
 
+[Adaptivity]
+  steps = 2
+  marker = uniform
+  [./Markers]
+    [./uniform]
+      type = UniformMarker
+      mark = refine
+    [../]
+  [../]
+[]
+
+
 [Outputs]
   execute_on = 'timestep_end'
   exodus = true

test/tests/variables/fe_hermite_convergence/hermite_converge_dirichlet_out.csv

@@ -0,0 +1,4 @@
+time,H1Semierror,H1error,L2error,dofs,h
+1,0.074775053298366,0.074924715366233,0.0047333262023076,116,0.70710678118655
+2,0.011349257396992,0.011356952857997,0.00041801286535784,388,0.35355339059327
+3,0.0015118325178008,0.0015121167524912,2.9317422887085e-05,1412,0.17677669529664

test/tests/variables/fe_hermite_convergence/hermite_converge_periodic.i

@@ -20,15 +20,6 @@
     grad_x = -pi*cos(pi*x)*sin(pi*y)
     grad_y = -pi*sin(pi*x)*cos(pi*y)
   [../]
-
-  [./bc_fnr]
-    type = ParsedFunction
-    value = -pi*cos(pi*x)*sin(pi*y)
-  [../]
-  [./bc_fnl]
-    type = ParsedFunction
-    value = pi*cos(pi*x)*sin(pi*y)
-  [../]
   [./bc_fnt]
     type = ParsedFunction
     value = -pi*sin(pi*x)*cos(pi*y)
@@ -37,7 +28,6 @@
     type = ParsedFunction
     value = pi*sin(pi*x)*cos(pi*y)
   [../]
-
   [./forcing_fn]
     type = ParsedFunction
     value = -2*pi*pi*sin(pi*x)*sin(pi*y)-sin(pi*x)*sin(pi*y)
@@ -57,12 +47,10 @@
     type = Diffusion
     variable = u
   [../]
-
   [./reaction]
     type = Reaction
     variable = u
   [../]
-
   [./forcing]
     type = BodyForce
     variable = u
@@ -71,30 +59,12 @@
 []
 
 [BCs]
-#  [./all]
-#    type = FunctionDirichletBC
-#    variable = u
-#    boundary = 'bottom right top left'
-#    function = bc_fn
-#  [../]
   [./Periodic]
     [./all]
       variable = u
       auto_direction= 'x y'
     [../]
   [../]
-  [./bc_right]
-    type=FunctionNeumannBC
-    variable = u
-    boundary = 'right'
-    function = bc_fnr
-  [../]
-  [./bc_left]
-    type=FunctionNeumannBC
-    variable = u
-    boundary = 'left'
-    function = bc_fnl
-  [../]
   [./bc_top]
     type=FunctionNeumannBC
     variable = u
@@ -113,12 +83,10 @@
   [./dofs]
     type = NumDOFs
   [../]
-
   [./h]
     type = AverageElementSize
     variable = u
   [../]
-
   [./L2error]
     type = ElementL2Error
     variable = u
@@ -138,17 +106,23 @@
 
 [Executioner]
   type = Steady
-
   solve_type = 'NEWTON'
 
-  [./Adaptivity]
-    steps = 2
-    refine_fraction = 1
-    coarsen_fraction = 0
-    max_h_level = 10
-  [../]
+  # We use higher-order quadrature to ensure that the forcing function
+  # is integrated accurately.
   [./Quadrature]
-    order=FIFTEENTH
+    order=ELEVENTH
+  [../]
+[]
+
+[Adaptivity]
+  steps = 2
+  marker = uniform
+  [./Markers]
+    [./uniform]
+      type = UniformMarker
+      mark = refine
+    [../]
   [../]
 []
 

test/tests/variables/fe_hermite_convergence/hermite_converge_periodic_out.csv

@@ -0,0 +1,4 @@
+time,H1Semierror,H1error,L2error,dofs,h
+1,0.074775053282849,0.074924715349675,0.0047333261853512,116,0.70710678118655
+2,0.011349257394713,0.011356952855582,0.00041801286158565,388,0.35355339059327
+3,0.0015118325174985,0.0015121167521718,2.9317421998023e-05,1412,0.17677669529664

test/tests/variables/fe_hermite_convergence/plot.py

@@ -0,0 +1,35 @@
+#!/usr/bin/env python
+import matplotlib.pyplot as plt
+import numpy as np
+
+"""
+This script makes log-log plots of the error vs. h for the tests in this directory.
+"""
+
+filenames = ['hermite_converge_dirichlet_out.csv',
+             'hermite_converge_periodic_out.csv']
+
+for filename in filenames:
+    fig = plt.figure()
+    ax1 = fig.add_subplot(111)
+
+    # passing names=True option is supposed to treat first row as column
+    # header names, and then everything is stored by column name in data.
+    data = np.genfromtxt(filename, delimiter=',', names=True)
+
+    log_h1_error = np.log10(data['H1error'])
+    log_l2_error = np.log10(data['L2error'])
+    logh = np.log10(data['h'])
+
+    h1_fit = np.polyfit(logh, log_h1_error, 1)
+    l2_fit = np.polyfit(logh, log_l2_error, 1)
+
+    ax1.plot(logh, log_h1_error, linewidth=2, marker='o', label=r'$H^1$ error')
+    ax1.text(-0.4, -2., '{:.2f}'.format(h1_fit[0]))
+
+    ax1.plot(logh, log_l2_error, linewidth=2, marker='o', label=r'$L^2$ error')
+    ax1.text(-0.4, -3.5, '{:.2f}'.format(l2_fit[0]))
+
+    ax1.set_xlabel('log(h)')
+    ax1.legend(loc='upper left')
+    plt.savefig(filename.rsplit( ".", 1)[0] + '.pdf')

test/tests/variables/fe_hermite_convergence/tests

@@ -7,10 +7,11 @@
     valgrind = 'HEAVY'
   [../]
 
-  [./test_hermite_converge_neumann]
+  [./test_hermite_converge_dirichlet]
     type = 'Exodiff'
-    input = 'hermite_converge_neumann.i'
-    exodiff = 'hermite_converge_neumann_out.e-s003'
+    input = 'hermite_converge_dirichlet.i'
+    exodiff = 'hermite_converge_dirichlet_out.e-s003'
     valgrind = 'HEAVY'
+    abs_zero = 1e-09
   [../]
 []