MFEML2Error

Overview

Postprocessor for calculating the L2 error of a scalar $var element = document.getElementById("moose-equation-e67106f5-aa19-40fd-abc6-8e5f75af3dbd");katex.render("H^1", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ or $var element = document.getElementById("moose-equation-f6294122-1160-43d0-950d-1845f524123b");katex.render("L^2", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ conforming source variable compared to a scalar function.

var element = document.getElementById("moose-equation-6043b508-7900-4c58-8c61-f0603fa2fdce");katex.render("\\left\\Vert u_{ex} - u_{h}\\right\\Vert_{\\mathrm{L2}}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

where $var element = document.getElementById("moose-equation-e47165d5-5f27-4d20-b234-f14e2dd75c3c");katex.render("u_{h} \\in H^1 \\lor L^2", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-eddc227d-f2be-4ca8-b43b-9ea05dcebbf6");katex.render("u_{ex}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a scalar function.

Example Input File Syntax

[Postprocessors<<<{"href": "../../../syntax/Postprocessors/index.html"}>>>]
  [potential_error]
    type = MFEML2Error<<<{"description": "Computes L2 error $\\left\\Vert u_{ex} - u_{h}\\right\\Vert_{\\rm L2}$ for gridfunctions using H1 or L2 elements.", "href": "MFEML2Error.html"}>>>
    variable<<<{"description": "Name of the variable of which to find the norm of the error."}>>> = velocity_potential
    function<<<{"description": "The analytic solution to compare against. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a number."}>>> = theta
  []
  [velocity_error]
    type = MFEMVectorL2Error<<<{"description": "Computes L2 error $\\left\\Vert \\vec u_{ex} - \\vec u_{h}\\right\\Vert_{\\rm L2}$ for vector gridfunctions.", "href": "MFEMVectorL2Error.html"}>>>
    variable<<<{"description": "Name of the vector variable of which to find the norm of the error."}>>> = velocity
    function<<<{"description": "The analytic solution to compare against. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a numeric vector value (enclosed in curly braces)."}>>> = exact_velocity
  []
[]

Input Parameters

variableName of the variable of which to find the norm of the error.
C++ Type:VariableName
Unit:(no unit assumed)
Controllable:No
Description:Name of the variable of which to find the norm of the error.

Required Parameters

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
Options:XFEM_MARK, FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, LINEAR_CONVERGENCE, NONLINEAR, NONLINEAR_CONVERGENCE, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, MULTIAPP_FIXED_POINT_CONVERGENCE, FINAL, CUSTOM
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.
functionThe analytic solution to compare against. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a number.
C++ Type:MFEMScalarCoefficientName
Controllable:No
Description:The analytic solution to compare against. A functor is any of the following: a variable, an MFEM material property, a function, a postprocessor or a number.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
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
Controllable:No
Description:Set the enabled status of the MooseObject.
outputsVector of output names where you would like to restrict the output of variables(s) associated with this object
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Advanced Parameters

Input Files

(test/tests/mfem/kernels/diffusion_amr.i)
(test/tests/mfem/kernels/irrotational.i)
(test/tests/mfem/kernels/darcy.i)
(test/tests/mfem/transfers/l2_mfem_parent_libmesh_sub/mfem_parent_scalar.i)
(test/tests/mfem/functions/parsed_function_source.i)
(test/tests/mfem/transfers/h1_mfem_parent_libmesh_sub/mfem_parent_scalar.i)

(test/tests/mfem/kernels/irrotational.i)

# 2D irrotational vortex with Nedelec elements of the first kind.

centre_x = -0.75
centre_y = 0.1

[Mesh]
  type = MFEMMesh
  file = ../mesh/vortex.msh
  dim = 2
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = SEVENTH
  []
  [HCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = SEVENTH
  []
[]

[Variables]
  [velocity_potential]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[AuxVariables]
  [velocity]
    type = MFEMVariable
    fespace = HCurlFESpace
  []
[]

[Functions]
  [speed]
    type = ParsedFunction
    expression = '1 / sqrt((x-x0)^2 + (y-y0)^2)'
    symbol_names = 'x0 y0'
  symbol_values = '${centre_x} ${centre_y}'
  []
  [theta]
    type = ParsedFunction
    expression = 'atan2(y-y0, x-x0)'
    symbol_names = 'x0 y0'
    symbol_values = '${centre_x} ${centre_y}'
  []
  [exact_velocity]
    type = ParsedVectorFunction
    expression_x = '-v * sin(th)'
    expression_y = 'v * cos(th)'
    symbol_names = 'v th'
    symbol_values = 'speed theta'
  []
[]

[BCs]
  [potential_velocity_boundary]
    type = MFEMScalarDirichletBC
    variable = velocity_potential
    boundary = '1'
    coefficient = theta
  []
[]

[Kernels]
  [laplacian]
    type = MFEMDiffusionKernel
    variable = velocity_potential
  []
[]

[AuxKernels]
  [grad]
    type = MFEMGradAux
    variable = velocity
    source = velocity_potential
    execute_on = TIMESTEP_END
  []
[]

[Preconditioner]
  [boomeramg]
    type = MFEMHypreBoomerAMG
  []
[]

[Solver]
  type = MFEMHypreGMRES
  preconditioner = boomeramg
  l_tol = 1e-16
  l_max_its = 1000
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[Postprocessors]
  [potential_error]
    type = MFEML2Error
    variable = velocity_potential
    function = theta
  []
  [velocity_error]
    type = MFEMVectorL2Error
    variable = velocity
    function = exact_velocity
  []
[]

[Outputs]
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/Irrotational
    vtk_format = ASCII
  []
  [L2CSV]
    type = CSV
    file_base = OutputData/Irrotational
  []
[]

(test/tests/mfem/kernels/diffusion_amr.i)

[Mesh]
  type = MFEMMesh
  file = ../mesh/square.msh
  nonconforming = true
[]

[Adaptivity]
  [Indicators]
    [l2zz]
      type = MFEML2ZienkiewiczZhuIndicator
      variable = concentration
      kernel = diff
    []
  []
  [Markers]
    [ref]
      type = MFEMRefinementMarker
      threshold = 0.7
      indicator = l2zz
      max_h_level = 1
    []
  []
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
  []
  [HCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = FIRST
  []
[]

[Variables]
  [concentration]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[AuxVariables]
  [concentration_gradient]
    type = MFEMVariable
    fespace = HCurlFESpace
  []
[]

[AuxKernels]
  [grad]
    type = MFEMGradAux
    variable = concentration_gradient
    source = concentration
    execute_on = TIMESTEP_END
  []
[]

[BCs]
  [top]
    type = MFEMScalarDirichletBC
    variable = concentration
    boundary = 4
    coefficient = 1
  []
  [bottom]
    type = MFEMScalarDirichletBC
    variable = concentration
    boundary = 2
  []
[]

[Functions]
  [D]
    type = ParsedFunction
    expression = 1+1/(1+exp(20*y-10))
  []
  [solution]
    type = ParsedFunction
    expression = (20*y+log(exp(20*y)+2*exp(10))-log(1+2*exp(10)))/(30+log(2+exp(10))-log(1+2*exp(10)))
  []
[]

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = concentration
    coefficient = D
  []
[]

[Preconditioner]
  [boomeramg]
    type = MFEMHypreBoomerAMG
  []
[]

[Solver]
  type = MFEMHypreGMRES
  preconditioner = boomeramg
  l_tol = 1e-16
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[Postprocessors]
  [error]
    type = MFEML2Error
    variable = concentration
    function = solution
  []
[]

[Outputs]
  csv = true
  file_base = OutputData/DiffusionHRefinement
[]

(test/tests/mfem/kernels/irrotational.i)

# 2D irrotational vortex with Nedelec elements of the first kind.

centre_x = -0.75
centre_y = 0.1

[Mesh]
  type = MFEMMesh
  file = ../mesh/vortex.msh
  dim = 2
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = SEVENTH
  []
  [HCurlFESpace]
    type = MFEMVectorFESpace
    fec_type = ND
    fec_order = SEVENTH
  []
[]

[Variables]
  [velocity_potential]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[AuxVariables]
  [velocity]
    type = MFEMVariable
    fespace = HCurlFESpace
  []
[]

[Functions]
  [speed]
    type = ParsedFunction
    expression = '1 / sqrt((x-x0)^2 + (y-y0)^2)'
    symbol_names = 'x0 y0'
  symbol_values = '${centre_x} ${centre_y}'
  []
  [theta]
    type = ParsedFunction
    expression = 'atan2(y-y0, x-x0)'
    symbol_names = 'x0 y0'
    symbol_values = '${centre_x} ${centre_y}'
  []
  [exact_velocity]
    type = ParsedVectorFunction
    expression_x = '-v * sin(th)'
    expression_y = 'v * cos(th)'
    symbol_names = 'v th'
    symbol_values = 'speed theta'
  []
[]

[BCs]
  [potential_velocity_boundary]
    type = MFEMScalarDirichletBC
    variable = velocity_potential
    boundary = '1'
    coefficient = theta
  []
[]

[Kernels]
  [laplacian]
    type = MFEMDiffusionKernel
    variable = velocity_potential
  []
[]

[AuxKernels]
  [grad]
    type = MFEMGradAux
    variable = velocity
    source = velocity_potential
    execute_on = TIMESTEP_END
  []
[]

[Preconditioner]
  [boomeramg]
    type = MFEMHypreBoomerAMG
  []
[]

[Solver]
  type = MFEMHypreGMRES
  preconditioner = boomeramg
  l_tol = 1e-16
  l_max_its = 1000
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[Postprocessors]
  [potential_error]
    type = MFEML2Error
    variable = velocity_potential
    function = theta
  []
  [velocity_error]
    type = MFEMVectorL2Error
    variable = velocity
    function = exact_velocity
  []
[]

[Outputs]
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/Irrotational
    vtk_format = ASCII
  []
  [L2CSV]
    type = CSV
    file_base = OutputData/Irrotational
  []
[]

(test/tests/mfem/kernels/darcy.i)

[Mesh]
  type = MFEMMesh
  file = ../mesh/star.mesh
  uniform_refine = 2
[]

[Problem]
  type = MFEMProblem
[]

[Functions]
  [exact_velocity]
    type = ParsedVectorFunction
    expression_x = '-exp(x) * sin(y)'
    expression_y = '-exp(x) * cos(y)'
  []
  [exact_pressure]
    type = ParsedFunction
    expression = 'exp(x) * sin(y)'
  []
  [exact_pressure_rhs]
    type = ParsedFunction
    expression = '-exp(x) * sin(y)'
  []
[]

[FESpaces]
  [HDivFESpace]
    type = MFEMVectorFESpace
    fec_type = RT
    fec_order = SECOND
  []
  [L2FESpace]
    type = MFEMScalarFESpace
    fec_type = L2
    fec_order = SECOND
    basis = GaussLegendre
  []
[]

[Variables]
  [velocity]
    type = MFEMVariable
    fespace = HDivFESpace
  []
  [pressure]
    type = MFEMVariable
    fespace = L2FESpace
  []
[]

[BCs]
  [flux_boundaries]
    type = MFEMVectorFEBoundaryFluxIntegratedBC
    variable = velocity
    coefficient = exact_pressure_rhs
  []
[]

[Kernels]
  [VelocityMass]
    type = MFEMVectorFEMassKernel
    variable = velocity
  []
  [PressureGrad]
    type = MFEMVectorFEDivergenceKernel
    trial_variable = pressure
    variable = velocity
    coefficient = -1
    transpose = true
  []
  [VelocityDiv]
    type = MFEMVectorFEDivergenceKernel
    trial_variable = velocity
    variable = pressure
    coefficient = -1
  []
[]

[Solver]
  type = MFEMMUMPS
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[Postprocessors]
  [velocity_error]
    type = MFEMVectorL2Error
    variable = velocity
    function = exact_velocity
  []
  [pressure_error]
    type = MFEML2Error
    variable = pressure
    function = exact_pressure
  []
[]

[Outputs]
  [ParaViewDataCollection]
    type = MFEMParaViewDataCollection
    file_base = OutputData/Darcy
    vtk_format = ASCII
  []
  [DarcyErrorCSV]
    type = CSV
    file_base = OutputData/Darcy
  []
[]

(test/tests/mfem/transfers/l2_mfem_parent_libmesh_sub/mfem_parent_scalar.i)

[Mesh]
  type = MFEMMesh
  file = ../../mesh/square_quad9.e
[]

[Problem]
  type = MFEMProblem
  solve = false
[]

[FESpaces]
  [L2FESpace]
    type = MFEMScalarFESpace
    fec_type = L2
    fec_order = CONSTANT
  []
[]

[Variables]
  [mfem_scalar_var]
    type = MFEMVariable
    fespace = L2FESpace
  []
[]

[AuxVariables]
  [libmesh_scalar_var]
    type = MFEMVariable
    fespace = L2FESpace
  []
[]

[Functions]
  [parsed_function]
    type = ParsedFunction
    expression = 'x*x + y*y'
  []
[]

[ICs]
  [libmesh_scalar_var_ic]
    type = MFEMScalarIC
    variable = 'mfem_scalar_var'
    coefficient = parsed_function
  []
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[MultiApps]
  [libmesh_app]
    type = FullSolveMultiApp
    input_files = libmesh_sub_scalar.i
    execute_on = 'INITIAL'
  []
[]

[Transfers]
  [transfer_from_libmesh]
    type = MultiApplibMeshToMFEMShapeEvaluationTransfer
    source_variables = libmesh_scalar_var
    variables = libmesh_scalar_var
    from_multi_app = libmesh_app
  []
[]

[Postprocessors]
  [Difference]
    type = MFEML2Error
    variable = mfem_scalar_var
    function = libmesh_scalar_var
    execute_on = TIMESTEP_END
  []
[]

[Outputs]
  file_base = 'mfem_parent_libmesh_sub_scalar_quads'
  csv = true
[]

(test/tests/mfem/functions/parsed_function_source.i)

[Mesh]
  type = MFEMMesh
  file = ../mesh/hinomaru.e
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
  []
[]

[Variables]
  [variable]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[ICs]
  [ic]
    type = MFEMScalarIC
    variable = variable
    coefficient = material
  []
[]

[BCs]
  [bc]
    type = MFEMScalarDirichletBC
    variable = variable
    boundary = skin
  []
[]

[FunctorMaterials]
  [material]
    type = MFEMGenericFunctorMaterial
    prop_names = material
    prop_values = -100
  []
[]

[Functions]
  [r]
    type = ParsedFunction
    expression = hypot(x,y)
  []
  [p]
    type = ParsedFunction
    expression = atan2(y,x)
  []
  [source]
    type = MFEMParsedFunction
    expression = v*sin(w*p)
    symbol_names = 'p w v'
    symbol_values = 'p 4 variable'
  []
  [solution]
    type = MFEMParsedFunction
    expression = if(r<=1,-c*sin(w*p)*(r^w-r^2)/(w^2-4),0)
    symbol_names = 'r p w c'
    symbol_values = 'r p 4 material'
  []
[]

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = variable
  []
  [source]
    type = MFEMDomainLFKernel
    variable = variable
    coefficient = source
    block = wire
  []
[]

[Preconditioner]
  [boomeramg]
    type = MFEMHypreBoomerAMG
  []
[]

[Solver]
  type = MFEMHyprePCG
  preconditioner = boomeramg
  l_tol = 1e-16
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[Postprocessors]
  [error]
    type = MFEML2Error
    variable = variable
    function = solution
  []
[]

[Outputs]
  csv = true
  file_base = OutputData/ParsedFunctionSource
[]

(test/tests/mfem/transfers/h1_mfem_parent_libmesh_sub/mfem_parent_scalar.i)

[Mesh]
  type = MFEMMesh
  file = ../../mesh/square_quad9.e
[]

[Problem]
  type = MFEMProblem
[]

[FESpaces]
  [H1FESpace]
    type = MFEMScalarFESpace
    fec_type = H1
    fec_order = FIRST
  []
[]

[Variables]
  [mfem_scalar_var]
    type = MFEMVariable
    fespace = H1FESpace
  []
  [libmesh_scalar_var]
    type = MFEMVariable
    fespace = H1FESpace
  []
[]

[BCs]
  [sides]
    type = MFEMScalarDirichletBC
    variable = mfem_scalar_var
    coefficient = 1.0
  []
[]

[Kernels]
  [diff]
    type = MFEMDiffusionKernel
    variable = mfem_scalar_var
  []
  [source]
    type = MFEMDomainLFKernel
    variable = mfem_scalar_var
    coefficient = 2.0
  []
[]

[Preconditioner]
  [boomeramg]
    type = MFEMHypreBoomerAMG
  []
  [jacobi]
    type = MFEMOperatorJacobiSmoother
  []
[]

[Solver]
  type = MFEMHypreGMRES
  preconditioner = boomeramg
  l_tol = 1e-12
  l_max_its = 1000
[]

[Executioner]
  type = MFEMSteady
  device = cpu
[]

[MultiApps]
  [libmesh_app]
    type = FullSolveMultiApp
    input_files = libmesh_sub_scalar.i
    execute_on = 'INITIAL'
  []
[]

[Transfers]
  [transfer_from_libmesh]
    type = MultiApplibMeshToMFEMShapeEvaluationTransfer
    source_variables = libmesh_scalar_var
    variables = libmesh_scalar_var
    from_multi_app = libmesh_app
  []
[]

[Postprocessors]
  [Difference]
    type = MFEML2Error
    variable = mfem_scalar_var
    function = libmesh_scalar_var
    execute_on = TIMESTEP_END
  []
[]

[Outputs]
  file_base = 'mfem_parent_libmesh_sub_scalar_quads'
  csv = true
[]

Overview
Example Input File Syntax
Input Parameters
Input Files