ElementH1SemiError

Returns the gradient difference norm part of the H1 error

The gradient of the variable is compared to the gradient of the specified function. Examining the error on the gradient can reveal excessive oscillations, highlight the need for a higher order finite element family, or show that the gradient of a known solution is well captured by the numerical solution.

var element = document.getElementById("moose-equation-e4c32c60-7542-4773-8059-84130895237b");katex.render("|u - f|_{H_1} = \\left( \\int_\\Omega \\left(\\nabla u(x,t) - \\nabla f(x,t) \\right)^p d\\Omega \\right)^{\\dfrac{1}{p}}", element, {displayMode:true,throwOnError:false});

where $var element = document.getElementById("moose-equation-d2056a65-c6c5-4b01-9587-5a802b47e8e1");katex.render("u", element, {displayMode:false,throwOnError:false});$ is the variable, $var element = document.getElementById("moose-equation-1617b798-a7ed-4a2c-ba75-95c9b1a5c384");katex.render("f", element, {displayMode:false,throwOnError:false});$ the function, $var element = document.getElementById("moose-equation-c68f5a95-186b-4c6c-81da-c8e9f046c242");katex.render("p", element, {displayMode:false,throwOnError:false});$ the norm exponent and $var element = document.getElementById("moose-equation-5044fb87-0cb8-4b57-8af1-e83dfe77a2da");katex.render("\\Omega", element, {displayMode:false,throwOnError:false});$ the integration domain, which may be limited to certain blocks using the block parameter.

Example input syntax

In this example, we compute a variety of error with the H1, L2 and H1-semi norms to verify that the H1 error is the sum of the L2 error and the H1-semi error.

[Postprocessors<<<{"href": "../../syntax/Postprocessors/index.html"}>>>]
  [dofs]
    type = NumDOFs<<<{"description": "Return the number of Degrees of freedom from either the NL, Aux or both systems.", "href": "NumDOFs.html"}>>>
    execute_on<<<{"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."}>>> = 'initial timestep_end'
  []

  [h1_error]
    type = ElementH1Error<<<{"description": "Computes the H1 error between a variable and a function", "href": "ElementH1Error.html"}>>>
    variable<<<{"description": "The name of the variable that this object operates on"}>>> = u
    function<<<{"description": "The analytic solution to compare against"}>>> = u_func
    execute_on<<<{"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."}>>> = 'initial timestep_end'
  []

  [h1_semi]
    type = ElementH1SemiError<<<{"description": "Returns the gradient difference norm part of the H1 error", "href": "ElementH1SemiError.html"}>>>
    variable<<<{"description": "The name of the variable that this object operates on"}>>> = u
    function<<<{"description": "The analytic solution to compare against"}>>> = u_func
    execute_on<<<{"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."}>>> = 'initial timestep_end'
  []

  [l2_error]
    type = ElementL2Error<<<{"description": "Computes L2 error between a field variable and an analytical function", "href": "ElementL2Error.html"}>>>
    variable<<<{"description": "The name of the variable that this object operates on"}>>> = u
    function<<<{"description": "The analytic solution to compare against"}>>> = u_func
    execute_on<<<{"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."}>>> = 'initial timestep_end'
  []
[]

Input Parameters

functionThe analytic solution to compare against
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The analytic solution to compare against
variableThe name of the variable that this object operates on
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this object operates on

Required Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
use_absolute_valueFalseWhether to use absolute value of the variable or not
Default:False
C++ Type:bool
Controllable:No
Description:Whether to use absolute value of the variable or not

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
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).
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, 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, 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.
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
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
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
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
Controllable:No
Description:Forces the UserObject to be executed in PREIC during initial setup

Execution Scheduling 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:Yes
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
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>
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
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
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

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
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.

Material Property Retrieval Parameters

(moose/test/tests/postprocessors/element_h1_error_pps/element_h1_error_pp_test.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 3
  ny = 3

  xmin = 0
  xmax = 2

  ymin = 0
  ymax = 2
[]

[Variables]
  active = 'u'

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

[Functions]
  active = 'forcing_func u_func'

  [forcing_func]
    type = ParsedFunction
    expression = alpha*alpha*pi*pi*sin(alpha*pi*x)
    symbol_names = 'alpha'
    symbol_values = '4'
  []

  [u_func]
    type = ParsedGradFunction
    expression = sin(alpha*pi*x)
    grad_x = alpha*pi*cos(alpha*pi*x)
    symbol_names = 'alpha'
    symbol_values = '4'
  []
[]

[Kernels]
  active = 'diff forcing'

  [diff]
    type = Diffusion
    variable = u
  []

  [forcing]
    type = BodyForce
    variable = u
    function = forcing_func
  []
[]

[BCs]
  active = 'left right'

  [left]
    type = DirichletBC
    variable = u
    boundary = '1'
    value = 0
  []

  [right]
    type = DirichletBC
    variable = u
    boundary = '3'
    value = 0
  []
[]

[Executioner]
  type = Steady

  [Adaptivity]
    refine_fraction = 1.0
    coarsen_fraction = 0.0
    max_h_level = 10
    steps = 4
  []
[]

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

  [h1_error]
    type = ElementH1Error
    variable = u
    function = u_func
    execute_on = 'initial timestep_end'
  []

  [h1_semi]
    type = ElementH1SemiError
    variable = u
    function = u_func
    execute_on = 'initial timestep_end'
  []

  [l2_error]
    type = ElementL2Error
    variable = u
    function = u_func
    execute_on = 'initial timestep_end'
  []
[]

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

Example input syntax
Input Parameters