2D negative-jacobian tests added

These tests ensure that in 2D:
 - when use_displaced_mesh=false, and when an element is inverted, MOOSE will not throw an error;
 - when use_displaced_mesh=false, and when an element is distorted to have exactly zero element-Jacobian, MOOSE will not throw an error;
 - when use_displaced_mesh=true, and when an element is distorted to have exactly zero element-Jacobian, MOOSE correctly will throw an error

The tests do NOT test in 2D:
 - when use_displaced_mesh=true, and when an element is inverted to produce a negative element-Jacobian, MOOSE correctly throws an error.
See lengthy discussion at idaholab#10229

Refs idaholab#9740

test/tests/misc/jacobian/no_negative_jacobian_2D.i

@@ -0,0 +1,42 @@
+# The 2D mesh is inverted using a prescribed displacement.
+# However, due to use_displaced_mesh = false in the Kernel,
+# libMesh does not throw a "negative jacobian" error
+[Mesh]
+  type = GeneratedMesh
+  dim = 2
+  displacements = 'disp_x disp_y'
+[]
+
+[AuxVariables]
+  [./disp_x]
+  [../]
+  [./disp_y]
+  [../]
+[]
+
+[AuxKernels]
+  [./disp_x]
+    variable = disp_x
+    type = FunctionAux
+    function = '-x*t'
+  [../]
+[]
+
+[Variables]
+  [./u]
+  [../]
+[]
+
+[Kernels]
+  [./diff]
+    type = Diffusion
+    variable = u
+    use_displaced_mesh = false
+  [../]
+[]
+
+[Executioner]
+  type = Transient
+  dt = 0.8
+  end_time = 1.5
+[]

test/tests/misc/jacobian/tests

@@ -38,18 +38,17 @@
     type = RunApp
     input = no_negative_jacobian.i
     issues = '#9740'
-    requirement = 'A simulation shall run fine if there are no negative element Jacobians'
+    requirement = 'If use_displaced_mesh = false then MOOSE will not throw an exception if elements are inverted to produce a negative element Jacobian, in 3D simulations'
   [../]
   [./jacobian_zero]
     type = RunException
     input = no_negative_jacobian.i
     prereq = no_negative_jacobian
-    # num_steps takes precendence over the end_time in the input file.
     cli_args = 'Kernels/diff/use_displaced_mesh=true Executioner/num_steps=2'
     expect_err = 'ERROR: negative Jacobian 0 at point \(x,y,z\)=\(       0, 0.211325, 0.211325\) in element 0'
     should_crash = False
     issues = '#9740'
-    requirement = 'A simulation shall throw an exception if there is a zero element Jacobians'
+    requirement = 'A 3D simulation shall throw an exception if there is a zero element Jacobian, when use_displaced_mesh = true'
   [../]
   [./jacobian_negative]
     type = RunException
@@ -60,10 +59,35 @@
     expect_err = 'ERROR: negative Jacobian -0.0625 at point \(x,y,z\)=\(-0.105662, 0.211325, 0.211325\) in element 0'
     should_crash = False
     issues = '#9740'
-    requirement = 'A simulation shall throw an exception if there is a negative element Jacobians'
+    requirement = 'A 3D simulation shall throw an exception if there is a negative element Jacobian, when use_displaced_mesh = true'
+  [../]
+
+  [./no_negative_jacobian_2D]
+    type = RunApp
+    input = no_negative_jacobian_2D.i
+    issues = '#9740 #10229'
+    requirement = 'If use_displaced_mesh = false then MOOSE will not throw an exception if elements are inverted to produce a negative element Jacobian, in 2D simulations'
+  [../]
+  [./zero_jacobian_2D_ok]
+    type = RunApp
+    input = no_negative_jacobian_2D.i
+    prereq = no_negative_jacobian_2D
+    cli_args = 'Executioner/dt=0.5'
+    issues = '#9740 #10229'
+    requirement = 'If use_displaced_mesh = false then MOOSE will not throw an exception if elements are distored to produce a zero element Jacobian, in 2D simulations'
+  [../]
+  [./jacobian_zero_2D]
+    type = RunException
+    input = no_negative_jacobian_2D.i
+    prereq = zero_jacobian_2D_ok
+    cli_args = 'Kernels/diff/use_displaced_mesh=true Executioner/dt=0.5 Executioner/num_steps=2'
+    expect_err = 'ERROR: negative Jacobian 0 at point \(x,y,z\)=\(       0, 0.211325,        0\) in element 0'
+    should_crash = False
+    issues = '#9740 #10229'
+    requirement = 'A 2D simulation shall throw an exception if there is a zero element Jacobian, when use_displaced_mesh = true'
   [../]
 
-  [./inf_nan]
+[./inf_nan]
     type = PetscJacobianTester
     input = 'inf_nan.i'
     recover = false