ElementL2ErrorFunctionAux

A class for computing the element-wise $var element = document.getElementById("moose-equation-b55f63a2-d76a-4035-aca7-1694e263963b");katex.render("L^2", element, {displayMode:false,throwOnError:false});$ error (actually $var element = document.getElementById("moose-equation-6c2d195e-33d9-418c-9b3d-9f235af0f074");katex.render("L^p", element, {displayMode:false,throwOnError:false});$ error, if you set the value of p to something other than 2) of the difference between an exact solution (typically represented by a ParsedFunction) and the coupled solution variable. The base class implements the compute() function.

Example syntax

[./l2_error_aux]
  type = ElementL2ErrorFunctionAux
  variable = element_l2_error
  # A function representing the exact solution for the solution
  function = exact_fn
  # The nonlinear variable representing the FEM solution
  coupled_variable = u
[../]

A class for computing the element-wise L^2 (Euclidean) error between a function and a coupled variable.

Input Parameters

coupled_variableThe variable to compute the norm of.
C++ Type:std::vector<VariableName>
Options:
Description:The variable to compute the norm of.
functionFunction representing the exact solution
C++ Type:FunctionName
Options:
Description:Function representing the exact solution
variableThe name of the variable that this object applies to
C++ Type:AuxVariableName
Options:
Description:The name of the variable that this object applies to

Required Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Options:
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this boundary condition applies
C++ Type:std::vector<BoundaryName>
Options:
Description:The list of boundaries (ids or names) from the mesh where this boundary condition applies
check_boundary_restrictedTrueWhether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
Default:True
C++ Type:bool
Options:
Description:Whether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
execute_onLINEAR TIMESTEP_ENDThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM, PRE_DISPLACE.
Default:LINEAR TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM, PRE_DISPLACE
Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM, PRE_DISPLACE.
p2The exponent used in the norm.
Default:2
C++ Type:double
Options:
Description:The exponent used in the norm.
prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Options:
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Options:
Description:The seed for the master random number generator
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Options:
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

(moose/test/tests/auxkernels/error_function_aux/error_function_aux.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 20
  ny = 20
[]

[Variables]
  [./u]
  [../]
[]

[AuxVariables]
  [./element_l2_error]
    # Aux field variable representing the L2 error on each element
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./element_h1_error]
    # Aux field variable representing the H1 error on each element
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./element_l2_norm]
    # Aux field variable representing the L^2 norm of the solution variable
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Functions]
  [./exact_fn]
    type = ParsedFunction
    value = sin(2*pi*x)*sin(2*pi*y)
  [../]

  [./forcing_fn]
    type = ParsedFunction
    value = 8*pi^2*sin(2*pi*x)*sin(2*pi*y)
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
  [./ffn]
    type = BodyForce
    variable = u
    function = forcing_fn
  [../]
[]

[AuxKernels]
  [./l2_norm_aux]
    type = ElementLpNormAux
    variable = element_l2_norm
    coupled_variable = u
  [../]
  [./l2_error_aux]
    type = ElementL2ErrorFunctionAux
    variable = element_l2_error
    # A function representing the exact solution for the solution
    function = exact_fn
    # The nonlinear variable representing the FEM solution
    coupled_variable = u
  [../]
  [./h1_error_aux]
    type = ElementH1ErrorFunctionAux
    variable = element_h1_error
    # A function representing the exact solution for the solution
    function = exact_fn
    # The nonlinear variable representing the FEM solution
    coupled_variable = u
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = 'bottom left right top'
    function = exact_fn
  [../]
[]

[Postprocessors]
  [./L2_error]
    # The L2 norm of the error over the entire mesh.  Note: this is
    # *not* equal to the sum over all the elements of the L2-error
    # norms.
    type = ElementL2Error
    variable = u
    function = exact_fn
  [../]
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

Example syntax
Input Parameters