Adding val-1e case

Ref: idaholab#12

doc/content/verification/val-1e.md

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+# val-1e
+
+# Diffusion in a composite layer
+Documentation is missing!
+
+### Notes
+
+The trapping test features some oscillations in the solution for whatever
+reason. In order for the oscillations to not take over the simulation, it seems
+that the ratio of the **inverse of the Fourier number** must be kept
+sufficiently high, e.g. `h^2 / (D * dt)`. Included in this directory are three
+`png` files that show the permeation for different `h` and `dt` values. They are
+summarized below:
+
+- `nx-80.png`: `nx = 80` and `dt = .0625`
+- `nx-40.png`: `nx = 40` and `dt = .25`
+- `nx-20.png`: `nx = 20` and `dt = 1`
+
+The oscillations in the permeation graph go away with increasing fineness in the
+mesh and in `dt`.
+
+!bibtex bibliography

test/tests/val-1e/tests

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+[Tests]
+  design = 'Diffusion.md TimeDerivative.md DirichletBC.md'
+  issues = '#12'
+  [exo]
+    type = Exodiff
+    input = val-1e.i
+    exodiff = val-1e_out.e
+    cli_args = 'Executioner/dt=1 Mesh/nx=198'
+    requirement = 'The system shall be able to model transient diffusion through a composite slab with a constant concentration boundary condition as the species source.'
+  []
+[]

test/tests/val-1e/val-1e.i

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+[Mesh]
+  type = GeneratedMesh
+  dim = 1
+  nx = 1000
+  xmax = 99e-6 #=========================
+[]
+
+[Variables]
+  [./u]
+  [../]
+[]
+
+[AuxVariables]
+  [./flux_x]
+    order = FIRST
+    family = MONOMIAL
+  [../]
+[]
+
+[Functions]
+  [diffusivity_value]
+    type = ParsedFunction
+    value = 'if(x<33e-6, 1.274e-7, 2.622e-11)' #=========================
+  []
+[]
+
+[Kernels]
+  [./diff]
+    type = Diffusion
+    variable = u
+  [../]
+  [./time]
+    type = TimeDerivative
+    variable = u
+  [../]
+[]
+
+[AuxKernels]
+  [./flux_x]
+    type = DiffusionFluxAux
+    diffusivity = diffusivity_value
+    variable = flux_x
+    diffusion_variable = u
+    component = x
+  [../]
+[]
+
+[BCs]
+  [./left]
+    type = DirichletBC
+    variable = u
+    boundary = left
+    value = 3.0537 #=========================
+  [../]
+  [./right]
+    type = DirichletBC
+    variable = u
+    boundary = right
+    value = 0
+  [../]
+[]
+
+[VectorPostprocessors]
+  [line]
+    type = LineValueSampler
+    start_point = '0 0 0'
+    end_point = '99e-6 0 0' #=========================
+    num_points = 199
+    sort_by = 'x'
+    variable = u
+  []
+[]
+
+[Postprocessors]
+  [conc_point1]
+    type = PointValue
+    variable = u
+    point = '40.5e-6 0 0'   #=========================
+  []
+  [flux_point2]
+    type = PointValue
+    variable = flux_x
+    point = '40.5e-6 0 0'  #=========================
+  []
+[]
+
+[Executioner]
+  type = Transient
+  end_time = 50
+  dt = .1
+  solve_type = NEWTON
+  petsc_options_iname = '-pc_type -pc_hypre_type'
+  petsc_options_value = 'hypre boomeramg'
+  l_tol = 1e-8
+  scheme = 'crank-nicolson'
+  nl_abs_tol = 1e-14  #=========================
+  automatic_scaling = true
+  compute_scaling_once = true
+[]
+
+[Outputs]
+  exodus = true
+  [csv]
+    type = CSV
+    interval = 10
+  []
+  perf_graph = true
+[]