PenaltyDirichletNodalKernel

Description

The PenaltyDirichletNodalKernel object is to apply Dirichlet boundary conditions using the penalty method for nodesets. It is similar to the PenaltyDirichletBC class which operates on sidesets.

Example Syntax

#In order to compare the solution generated using preset BC, the penalty was set to 1e10.
#Large penalty number should be used with caution.

[Mesh<<<{"href": "../../syntax/Mesh/index.html"}>>>]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  nx = 10
  ny = 10
  elem_type = QUAD4
[]

[Functions<<<{"href": "../../syntax/Functions/index.html"}>>>]
  [./forcing_fn]
    type = ParsedFunction<<<{"description": "Function created by parsing a string", "href": "../functions/MooseParsedFunction.html"}>>>
    expression<<<{"description": "The user defined function."}>>> = -2*(x*x+y*y-2)
  [../]

  [./solution]
    type = ParsedGradFunction<<<{"description": "Defines a function and its gradient using input file parameters.", "href": "../functions/MooseParsedGradFunction.html"}>>>
    value<<<{"description": "User defined function."}>>> = (1-x*x)*(1-y*y)
    grad_x<<<{"description": "Partial derivative with respect to x."}>>> = 2*(x*y*y-x)
    grad_y<<<{"description": "Partial derivative with respect to y."}>>> = 2*(x*x*y-y)
  [../]
[]

[Variables<<<{"href": "../../syntax/Variables/index.html"}>>>]
  [./u]
  [../]
[]

[Kernels<<<{"href": "../../syntax/Kernels/index.html"}>>>]
  [./diff]
    type = Diffusion<<<{"description": "The Laplacian operator ($-\\nabla \\cdot \\nabla u$), with the weak form of $(\\nabla \\phi_i, \\nabla u_h)$.", "href": "../kernels/Diffusion.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = u
  [../]
  [./forcing]
    type = BodyForce<<<{"description": "Demonstrates the multiple ways that scalar values can be introduced into kernels, e.g. (controllable) constants, functions, and postprocessors. Implements the weak form $(\\psi_i, -f)$.", "href": "../kernels/BodyForce.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = u
    function<<<{"description": "A function that describes the body force"}>>> = forcing_fn
  [../]
[]

[NodalKernels<<<{"href": "../../syntax/NodalKernels/index.html"}>>>]
  [./bc_all]
    type = PenaltyDirichletNodalKernel<<<{"description": "Enforces a Dirichlet boundary condition in a weak sense by penalizing differences between the current solution and the Dirichlet value on nodesets.", "href": "PenaltyDirichletNodalKernel.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = u
    value<<<{"description": "Boundary value of the variable"}>>> = 0
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = 'top left right bottom'
    penalty<<<{"description": "Penalty scalar"}>>> = 1e10
  [../]
[]

# [BCs]
#   [./fix]
#     type = DirichletBC
#     preset = true
#     variable = u
#     value = 0
#     boundary = 'top left right bottom'
#   [../]
# []

[Postprocessors<<<{"href": "../../syntax/Postprocessors/index.html"}>>>]
  [./L2error]
    type = ElementL2Error<<<{"description": "Computes L2 error between a field variable and an analytical function", "href": "../postprocessors/ElementL2Error.html"}>>>
    variable<<<{"description": "The name of the variable that this object operates on"}>>> = u
    function<<<{"description": "The analytic solution to compare against"}>>> = solution
  [../]
  [./H1error]
    type = ElementH1Error<<<{"description": "Computes the H1 error between a variable and a function", "href": "../postprocessors/ElementH1Error.html"}>>>
    variable<<<{"description": "The name of the variable that this object operates on"}>>> = u
    function<<<{"description": "The analytic solution to compare against"}>>> = solution
  [../]
  [./H1Semierror]
    type = ElementH1SemiError<<<{"description": "Returns the gradient difference norm part of the H1 error", "href": "../postprocessors/ElementH1SemiError.html"}>>>
    variable<<<{"description": "The name of the variable that this object operates on"}>>> = u
    function<<<{"description": "The analytic solution to compare against"}>>> = solution
  [../]
[]

[Executioner<<<{"href": "../../syntax/Executioner/index.html"}>>>]
  type = Steady
  solve_type = 'PJFNK'
  nl_rel_tol = 1e-14
[]

[Outputs<<<{"href": "../../syntax/Outputs/index.html"}>>>]
  file_base<<<{"description": "Common file base name to be utilized with all output objects"}>>> = nodal_preset_bc_out
  exodus<<<{"description": "Output the results using the default settings for Exodus output."}>>> = true
[]

Input Parameters