NodalL2Error

The L2-norm of the difference between a variable and a function computed at nodes.

This is typically used to compare a nodal variable to a known analytical solution. To compute the error with regards to a variable, instead of a function, you may use a ParsedAux to store the difference in an AuxVariable, then use the NodalL2Error or NodalL2Norm postprocessor to compute the norm.

Example input syntax

In this example, variable u is the solution of a diffusion-source problem. We know the analytical solution of this problem and use the NodalL2Error postprocessor to examine the quality of the numerical solution.

[Postprocessors<<<{"href": "../../syntax/Postprocessors/index.html"}>>>]
  [./l2_error]
    type = NodalL2Error<<<{"description": "The L2-norm of the difference between a variable and a function computed at nodes.", "href": "NodalL2Error.html"}>>>
    variable<<<{"description": "The name of the variable that this postprocessor operates on"}>>> = u
    function<<<{"description": "The analytic solution to compare against"}>>> = Soln
  [../]
[]

[Functions<<<{"href": "../../syntax/Functions/index.html"}>>>]
  [./dts]
    type = PiecewiseLinear<<<{"description": "Linearly interpolates between pairs of x-y data", "href": "../functions/PiecewiseLinear.html"}>>>
    x<<<{"description": "The abscissa values"}>>> = '0.01 0.1'
    y<<<{"description": "The ordinate values"}>>> = '0.005 0.05'
  [../]

  [./Soln]
    type = ParsedFunction<<<{"description": "Function created by parsing a string", "href": "../functions/MooseParsedFunction.html"}>>>
    expression<<<{"description": "The user defined function."}>>> = 't*(x*x+y*y)'
  [../]
  [./Source]
    type = ParsedFunction<<<{"description": "Function created by parsing a string", "href": "../functions/MooseParsedFunction.html"}>>>
    expression<<<{"description": "The user defined function."}>>> = '(x*x + y*y) - 4*t'
  [../]
  [./TopBC]
    type = ParsedFunction<<<{"description": "Function created by parsing a string", "href": "../functions/MooseParsedFunction.html"}>>>
    expression<<<{"description": "The user defined function."}>>> = 't*(x*x+1)'
  [../]
  [./BottomBC]
    type = ParsedFunction<<<{"description": "Function created by parsing a string", "href": "../functions/MooseParsedFunction.html"}>>>
    expression<<<{"description": "The user defined function."}>>> = 't*x*x'
  [../]
  [./RightBC]
    type = ParsedFunction<<<{"description": "Function created by parsing a string", "href": "../functions/MooseParsedFunction.html"}>>>
    expression<<<{"description": "The user defined function."}>>> = 't*(y*y+1)'
  [../]
  [./LeftBC]
    type = ParsedFunction<<<{"description": "Function created by parsing a string", "href": "../functions/MooseParsedFunction.html"}>>>
    expression<<<{"description": "The user defined function."}>>> = 't*y*y'
  [../]
[]

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 postprocessor operates on
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this postprocessor 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
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
unique_node_executeFalseWhen false (default), block restricted objects will have the execute method called multiple times on a single node if the node lies on a interface between two subdomains.
Default:False
C++ Type:bool
Controllable:No
Description:When false (default), block restricted objects will have the execute method called multiple times on a single node if the node lies on a interface between two subdomains.

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.
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

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

# This test covers the usage of the VariableTimeIntegrationAux
# kernel. Here we test three different schemes for integrating a field
# variable in time.  Midpoint, Trapezoidal, and Simpson's rule are
# used.  For this test, we use a manufactured solution and we compare
# the Trapezoidal and Simpson's rule, which must be exact for this
# exact solution, which is a linear function of time.
#
# The set up problem is
#
#  du/dt - Laplacian(u) = Q
#
# with exact solution: u = t*(x*x+y*y).
[Mesh]
  type = GeneratedMesh
  dim = 2
  elem_type = QUAD9
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 10
  ny = 10
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    x = '0.01 0.1'
    y = '0.005 0.05'
  [../]
[]

[Variables]
  [./u]
    initial_condition = 0.0
    family = LAGRANGE
    order = SECOND
  [../]
[]

[Kernels]
  [./diff]
     type = Diffusion
     variable = u
  [../]
  [./timederivative]
     type = TimeDerivative
     variable = u
  [../]
  [./sourceterm]
     type = BodyForce
     variable = u
     function = Source
  [../]
[]

[AuxVariables]
  [./v_midpoint]
  [../]
  [./v_trapazoid]
  [../]
  [./v_simpson]
  [../]
[]

[AuxKernels]
  [./MidpointTimeIntegrator]
    type = VariableTimeIntegrationAux
    variable_to_integrate = u
    variable = v_midpoint
    order = 1
  [../]
  [./TrapazoidalTimeIntegrator]
    type = VariableTimeIntegrationAux
    variable_to_integrate = u
    variable = v_trapazoid
    order = 2
  [../]
  [./SimpsonsTimeIntegrator]
    type = VariableTimeIntegrationAux
    variable_to_integrate = u
    variable = v_simpson
    order = 3
  [../]
[]

[BCs]
 [./RightBC]
    type = FunctionDirichletBC
    variable = u
    function = RightBC
    boundary = 'right'
 [../]
 [./LeftBC]
    type = FunctionDirichletBC
    variable = u
    function = LeftBC
    boundary = 'left'
 [../]
 [./TopBC]
    type = FunctionDirichletBC
    variable = u
    function = TopBC
    boundary = 'top'
 [../]
 [./BottomBC]
    type = FunctionDirichletBC
    variable = u
    function = BottomBC
    boundary = 'bottom'
 [../]
[]

[Functions]
 [./Soln]
    type = ParsedFunction
    expression = 't*(x*x+y*y)'
 [../]
 [./Source]
    type = ParsedFunction
    expression = '(x*x + y*y) - 4*t'
 [../]
 [./TopBC]
    type = ParsedFunction
    expression = 't*(x*x+1)'
 [../]
 [./BottomBC]
    type = ParsedFunction
    expression = 't*x*x'
 [../]
 [./RightBC]
   type = ParsedFunction
   expression = 't*(y*y+1)'
 [../]
 [./LeftBC]
    type = ParsedFunction
    expression = 't*y*y'
  [../]
[]
[Postprocessors]
  [./l2_error]
    type = NodalL2Error
    variable = u
    function = Soln
  [../]
[]

[Executioner]
  type = Transient

  end_time = 0.1
#  dt = 0.1
#  num_steps = 10
  [./TimeStepper]
     type = FunctionDT
     function = dts
  [../]

  nl_abs_tol = 1.e-15
[]

[Outputs]
  execute_on = 'timestep_end'
  exodus = true
[]

Example input syntax
Input Parameters