ElementVectorL2Error

Returns the L2-norm of the difference between a pair of computed and analytical vector-valued solutions.

Overview

The L2-error between a vector-valued solution $var element = document.getElementById("moose-equation-3c94d1c6-5265-45d0-9b6b-29bf141f4d12");katex.render("\\vec{u}", element, {displayMode:false,throwOnError:false});$ and a known vector-valued function $var element = document.getElementById("moose-equation-a958238b-9138-4c6f-9fdf-2b292fb70fe7");katex.render("\\vec{f}", element, {displayMode:false,throwOnError:false});$ is written

$var element = document.getElementById("moose-equation-a3b8ee8a-a731-46f8-988c-bb298c5a351c");katex.render(" \\left( \\int_{\\Omega} || \\vec{u} - \\vec{f} ||^2 \\,\\text{d}x \\right) ^{1/2}", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-d7722ea9-3138-4377-8700-feb4d3c5e189");katex.render("||\\cdot||", element, {displayMode:false,throwOnError:false});$ denotes the l2-norm in $var element = document.getElementById("moose-equation-714bad20-cbee-41af-917c-30286ccfd08c");katex.render("\\mathbb{R}^d", element, {displayMode:false,throwOnError:false});$ .

The user can specify $var element = document.getElementById("moose-equation-94c07a82-5873-4e47-a96b-e4fb6f2357e3");katex.render("\\vec{u}", element, {displayMode:false,throwOnError:false});$ with either a single nonlinear vector variable, or with up to three nonlinear scalar variables simultaneously, which would each typically represent the x, y, z components of the vector variable.

Likewise, the user can also specify $var element = document.getElementById("moose-equation-a558caf9-4ef3-4317-89b9-4edfd0359aeb");katex.render("\\vec{f}", element, {displayMode:false,throwOnError:false});$ with either a single Function object defining the vectorValue method, e.g. ParsedVectorFunction, or up to three such objects defining the value method, e.g. ParsedFunction.

Example Input File Syntax

With a single nonlinear vector variable and a single vector-valued function:

[Postprocessors]
  [L2Error]
    type = ElementVectorL2Error
    variable = u
    function = f
  []
[]

With component-wise specifications for both the nonlinear variable and the function:

[./integral]
  type = ElementVectorL2Error
  var_x = u
  var_y = v
  function_x = bc_u
  function_y = bc_v
  execute_on = 'initial timestep_end'
[../]

Input Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Unit:(no unit assumed)
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Unit:(no unit assumed)
Options:NONE, INITIAL, LINEAR, NONLINEAR_CONVERGENCE, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, TRANSFER
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
function0The vector analytical solution to compare against
Default:0
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The vector analytical solution to compare against
function_x0The analytical solution to compare against in the x direction
Default:0
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The analytical solution to compare against in the x direction
function_y0The analytical solution to compare against in the y direction
Default:0
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The analytical solution to compare against in the y direction
function_z0The analytical solution to compare against in the z direction
Default:0
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The analytical solution to compare against in the z direction
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
Unit:(no unit assumed)
Controllable:No
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.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
var_xThe FE solution in the x direction
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The FE solution in the x direction
var_yThe FE solution in the y direction
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The FE solution in the y direction
var_zThe FE solution in the z direction
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The FE solution in the z direction
variableThe vector FE solution
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The vector FE solution

Optional Parameters

allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:Yes
Description:Set the enabled status of the MooseObject.
execution_order_group0Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
Default:0
C++ Type:int
Unit:(no unit assumed)
Controllable:No
Description:Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
force_postauxFalseForces the UserObject to be executed in POSTAUX
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Forces the UserObject to be executed in POSTAUX
force_preauxFalseForces the UserObject to be executed in PREAUX
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Forces the UserObject to be executed in PREAUX
force_preicFalseForces the UserObject to be executed in PREIC during initial setup
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Forces the UserObject to be executed in PREIC during initial setup
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
outputsVector of output names where you would like to restrict the output of variables(s) associated with this object
C++ Type:std::vector<OutputName>
Unit:(no unit assumed)
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
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
Unit:(no unit assumed)
Controllable:No
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/kernels/vector_fe/coupled_electrostatics.i)

# Test for DivField and GradField kernels and VectorDivPenaltyDirichletBC bcs.
# This test uses Raviart-Thomas elements to solve a model div-grad problem
# in H(div). The problem is simply a div-grad formulation, u = -grad(p), and
# div(u) = f, of the standard Poisson problem div(grad(p)) = -f.
# Manufactured solution: p = cos(k*x)*sin(k*y)*cos(k*z).

k = asin(1)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 6
    ny = 6
    nz = 6
    xmax =  1
    ymax =  1
    zmax =  1
    xmin = -1
    ymin = -1
    zmin = -1
    elem_type = HEX27
  []
[]

[Variables]
  [u]
    family = RAVIART_THOMAS
    order = FIRST
  []
  [p]
    family = MONOMIAL
    order = CONSTANT
  []
  [lambda]
    family = SCALAR
    order = FIRST
  []
[]

[Functions]
  [f]
    type = ParsedVectorFunction
    expression_x =  ${k}*sin(${k}*x)*sin(${k}*y)*cos(${k}*z)
    expression_y = -${k}*cos(${k}*x)*cos(${k}*y)*cos(${k}*z)
    expression_z =  ${k}*cos(${k}*x)*sin(${k}*y)*sin(${k}*z)
    div = ${Mesh/gmg/dim}*${k}^2*cos(${k}*x)*sin(${k}*y)*cos(${k}*z)
  []
[]

[Kernels]
  [coefficient]
    type = VectorFunctionReaction
    variable = u
    sign = negative
  []
  [gradient]
    type = GradField
    variable = u
    coupled_scalar_variable = p
  []
  [divergence]
    type = DivField
    variable = p
    coupled_vector_variable = u
  []
  [forcing]
    type = BodyForce
    variable = p
    function = ${Functions/f/div}
  []
  [mean_zero_p]
    type = ScalarLagrangeMultiplier
    variable = p
    lambda = lambda
  []
[]

[ScalarKernels]
  [constraint]
    type = AverageValueConstraint
    variable = lambda
    pp_name = PP
    value = 0.0
  []
[]

[BCs]
  [sides]
    type = VectorDivPenaltyDirichletBC
    variable = u
    function = f
    penalty = 1e8
    boundary = 'top bottom left right front back'
  []
[]

[Postprocessors]
  active = PP
  [PP]
    type = ElementIntegralVariablePostprocessor
    variable = p
    execute_on = linear
  []
  [L2Error]
    type = ElementVectorL2Error
    variable = u
    function = f
  []
  [HDivSemiError]
    type = ElementHDivSemiError
    variable = u
    function = f
  []
  [HDivError]
    type = ElementHDivError
    variable = u
    function = f
  []
[]

[Preconditioning]
  [SMP]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Steady
  solve_type = LINEAR
  petsc_options_iname = '-pc_type -ksp_rtol -ksp_norm_type'
  petsc_options_value = '  jacobi     1e-12 preconditioned'
[]

[Outputs]
  exodus = true
[]

(moose/test/tests/postprocessors/element_vec_l2_error_pps/element_vec_l2_error.i)

[Mesh]
  type = GeneratedMesh
  dim = 2

  nx = 5
  ny = 5

  xmin = 0.0
  xmax = 1.0

  ymin = 0.0
  ymax = 1.0
[]

[Variables]
  active = 'u v'

  [./u]
    order = FIRST
    family = LAGRANGE
  [../]

  [./v]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Functions]
  active = 'bc_u bc_v f_u f_v'

  # A ParsedFunction allows us to supply analytic expressions
  # directly in the input file
  [./bc_u]
    type = ParsedFunction
    expression = sin(alpha*pi*x)
    symbol_names = 'alpha'
    symbol_values = '2'
  [../]

  [./bc_v]
    type = ParsedFunction
    expression = sin(alpha*pi*y)
    symbol_names = 'alpha'
    symbol_values = '2'
  [../]

  [./f_u]
    type = ParsedFunction
    expression = alpha*alpha*pi*pi*sin(alpha*pi*x)
    symbol_names = 'alpha'
    symbol_values = '2'
  [../]

  [./f_v]
    type = ParsedFunction
    expression = alpha*alpha*pi*pi*sin(alpha*pi*y)
    symbol_names = 'alpha'
    symbol_values = '2'
  [../]
[]

[Kernels]
  active = 'diff_u diff_v forcing_u forcing_v'

  [./diff_u]
    type = Diffusion
    variable = u
  [../]

  [./diff_v]
    type = Diffusion
    variable = v
  [../]

  # This Kernel can take a function name to use
  [./forcing_u]
    type = BodyForce
    variable = u
    function = f_u
  [../]

  [./forcing_v]
    type = BodyForce
    variable = v
    function = f_v
  [../]
[]

[BCs]
  active = 'all_u all_v'

  # The BC can take a function name to use
  [./all_u]
    type = FunctionDirichletBC
    variable = u
    boundary = 'bottom right top left'
    function = bc_u
  [../]

  [./all_v]
    type = FunctionDirichletBC
    variable = v
    boundary = 'bottom right top left'
    function = bc_v
  [../]
[]

[Executioner]
  type = Steady

  [./Adaptivity]
    refine_fraction = 1.0
    coarsen_fraction = 0.0
    max_h_level = 10
    steps = 3
  [../]
[]

[Postprocessors]
  [./dofs]
    type = NumDOFs
    execute_on = 'initial timestep_end'
  [../]

  [./integral]
    type = ElementVectorL2Error
    var_x = u
    var_y = v
    function_x = bc_u
    function_y = bc_v
    execute_on = 'initial timestep_end'
  [../]
[]

[Outputs]
  file_base = out
  exodus = false
  csv = true
[]

Overview
Example Input File Syntax
Input Parameters