ScalarL2Error

construction:Undocumented Class

The ScalarL2Error has not been documented. The content listed below should be used as a starting point for documenting the class, which includes the typical automatic documentation associated with a MooseObject; however, what is contained is ultimately determined by what is necessary to make the documentation clear for users.


# ScalarL2Error

!syntax description /Postprocessors/ScalarL2Error

## Overview

!! Replace these lines with information regarding the ScalarL2Error object.

## Example Input File Syntax

!! Describe and include an example of how to use the ScalarL2Error object.

!syntax parameters /Postprocessors/ScalarL2Error

!syntax inputs /Postprocessors/ScalarL2Error

!syntax children /Postprocessors/ScalarL2Error

Compute L2 error of a scalar variable using analytic function.

Input Parameters

functionThe analytic solution to compare against
C++ Type:FunctionName
Options:
Description:The analytic solution to compare against
variableThe name of the scalar variable
C++ Type:VariableName
Options:
Description:The name of the scalar variable

Required Parameters

execute_onTIMESTEP_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.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM, TRANSFER
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.

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
Options:
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>
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.
force_preauxFalseForces the GeneralUserObject to be executed in PREAUX
Default:False
C++ Type:bool
Options:
Description:Forces the GeneralUserObject to be executed in PREAUX
force_preicFalseForces the GeneralUserObject to be executed in PREIC during initial setup
Default:False
C++ Type:bool
Options:
Description:Forces the GeneralUserObject to be executed in PREIC during initial setup
outputsVector of output names were you would like to restrict the output of variables(s) associated with this object
C++ Type:std::vector<OutputName>
Options:
Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object
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

Input Files

(test/tests/kernels/ode/ode_sys_impl_test.i)
(examples/ex18_scalar_kernel/ex18_parsed.i)
(test/tests/time_integrators/scalar/scalar.i)
(test/tests/time_integrators/scalar/stiff.i)
(modules/tensor_mechanics/test/tests/global_strain/global_strain_hydrostat.i)
(test/tests/kernels/ode/parsedode_sys_impl_test.i)
(examples/ex18_scalar_kernel/ex18.i)
(test/tests/kernels/ode/parsedode_pp_test.i)
(test/tests/tag/scalar_tag_vector.i)
(test/tests/time_integrators/explicit_ssp_runge_kutta/explicit_ssp_runge_kutta.i)

(test/tests/kernels/ode/ode_sys_impl_test.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 2
  ny = 2
  elem_type = QUAD4
[]

[Functions]
  [./f_fn]
    type = ParsedFunction
    value = -4
  [../]
  [./bc_all_fn]
    type = ParsedFunction
    value = x*x+y*y
  [../]

  # ODEs
  [./exact_x_fn]
    type = ParsedFunction
    value = (-1/3)*exp(-t)+(4/3)*exp(5*t)
  [../]
[]

# NL

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

  # ODE variables
  [./x]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
  [./y]
    family = SCALAR
    order = FIRST
    initial_condition = 2
  [../]
[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = u
  [../]
  [./diff]
    type = Diffusion
    variable = u
  [../]
  [./uff]
    type = BodyForce
    variable = u
    function = f_fn
  [../]
[]

[ScalarKernels]
  [./td1]
    type = ODETimeDerivative
    variable = x
  [../]
  [./ode1]
    type = ImplicitODEx
    variable = x
    y = y
  [../]

  [./td2]
    type = ODETimeDerivative
    variable = y
  [../]
  [./ode2]
    type = ImplicitODEy
    variable = y
    x = x
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = '0 1 2 3'
    function = bc_all_fn
  [../]
[]

[Postprocessors]
  active = 'exact_x l2err_x x y'

  [./x]
    type = ScalarVariable
    variable = x
    execute_on = 'initial timestep_end'
  [../]
  [./y]
    type = ScalarVariable
    variable = y
    execute_on = 'initial timestep_end'
  [../]

  [./exact_x]
    type = FunctionValuePostprocessor
    function = exact_x_fn
    execute_on = 'initial timestep_end'
    point = '0 0 0'
  [../]

  [./l2err_x]
    type = ScalarL2Error
    variable = x
    function = exact_x_fn
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  start_time = 0
  dt = 0.01
  num_steps = 100

  solve_type = 'PJFNK'
[]

[Outputs]
  exodus = true
[]

(examples/ex18_scalar_kernel/ex18_parsed.i)

#
# Example 18 modified to use parsed ODE kernels.
#
# The ParsedODEKernel takes function expressions in the input file and computes
# Jacobian entries via automatic differentiation. It allows for rapid development
# of new models without the need for code recompilation.
#
# This input file should produce the exact same result as ex18.i
#

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 10
  ny = 10
  elem_type = QUAD4
[]

[Functions]
  # ODEs
  [./exact_x_fn]
    type = ParsedFunction
    value = (-1/3)*exp(-t)+(4/3)*exp(5*t)
  [../]
  [./exact_y_fn]
    type = ParsedFunction
    value = (2/3)*exp(-t)+(4/3)*exp(5*t)
  [../]
[]

[Variables]
  [./diffused]
    order = FIRST
    family = LAGRANGE
  [../]

  # ODE variables
  [./x]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
  [./y]
    family = SCALAR
    order = FIRST
    initial_condition = 2
  [../]

[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = diffused
  [../]
  [./diff]
    type = Diffusion
    variable = diffused
  [../]
[]

[ScalarKernels]
  [./td1]
    type = ODETimeDerivative
    variable = x
  [../]

  #
  # This parsed expression ODE Kernel behaves exactly as the ImplicitODEx kernel
  # in the main example. Checkout ImplicitODEx::computeQpResidual() in the
  # source code file ImplicitODEx.C to see the matching residual function.
  #
  # The ParsedODEKernel automaticaly generates the On- and Off-Diagonal Jacobian
  # entries.
  #
  [./ode1]
    type = ParsedODEKernel
    function = '-3*x - 2*y'
    variable = x
    args = y
  [../]

  [./td2]
    type = ODETimeDerivative
    variable = y
  [../]

  #
  # This parsed expression ODE Kernel behaves exactly as the ImplicitODEy Kernel
  # in the main example.
  #
  [./ode2]
    type = ParsedODEKernel
    function = '-4*x - y'
    variable = y
    args = x
  [../]
[]


[BCs]
  [./right]
    type = ScalarDirichletBC
    variable = diffused
    boundary = 1
    scalar_var = x
  [../]

  [./left]
    type = ScalarDirichletBC
    variable = diffused
    boundary = 3
    scalar_var = y
  [../]
[]

[Postprocessors]
  # to print the values of x, y into a file so we can plot it
  [./x]
    type = ScalarVariable
    variable = x
    execute_on = timestep_end
  [../]
  [./y]
    type = ScalarVariable
    variable = y
    execute_on = timestep_end
  [../]

  [./exact_x]
    type = FunctionValuePostprocessor
    function = exact_x_fn
    execute_on = timestep_end
  [../]

  [./exact_y]
    type = FunctionValuePostprocessor
    function = exact_y_fn
    execute_on = timestep_end
    point = '0 0 0'
  [../]

  # Measure the error in ODE solution for 'x'.
  [./l2err_x]
    type = ScalarL2Error
    variable = x
    function = exact_x_fn
  [../]

  # Measure the error in ODE solution for 'y'.
  [./l2err_y]
    type = ScalarL2Error
    variable = y
    function = exact_y_fn
  [../]
[]


[Executioner]
  type = Transient
  start_time = 0
  dt = 0.01
  num_steps = 10
  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = 'ex18_out'
  exodus = true
[]

(test/tests/time_integrators/scalar/scalar.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 1
  ny = 1
  elem_type = QUAD4
[]

[Variables]
  [./n]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
[]

[ScalarKernels]
  [./dn]
    type = ODETimeDerivative
    variable = n
  [../]
  [./ode1]
    type = ParsedODEKernel
    function = '-n'
    variable = n
    # implicit = false
  [../]
[]

[Executioner]
  type = Transient
  [./TimeIntegrator]
    # type = ImplicitEuler
    # type = BDF2
    type = CrankNicolson
    # type = ImplicitMidpoint
    # type = LStableDirk2
    # type = LStableDirk3
    # type = LStableDirk4
    # type = AStableDirk4
    #
    # Explicit methods
    # type = ExplicitEuler
    # type = ExplicitMidpoint
    # type = Heun
    # type = Ralston
  [../]
  start_time = 0
  end_time = 1
  dt = 0.001
  dtmin = 0.001 # Don't allow timestep cutting
  solve_type = 'PJFNK'
  nl_max_its = 2
  nl_abs_tol = 1.e-12 # This is an ODE, so nl_abs_tol makes sense.
[]

[Functions]
  [./exact_solution]
    type = ParsedFunction
    value = exp(t)
  [../]
[]

[Postprocessors]
  [./error_n]
    # Post processor that computes the difference between the computed
    # and exact solutions.  For the exact solution used here, the
    # error at the final time should converge at O(dt^p), where p is
    # the order of the method.
    type = ScalarL2Error
    variable = n
    function = exact_solution
    # final is not currently supported for Postprocessor execute_on...
    # execute_on = 'final'
  [../]
[]

[Outputs]
  csv = true
[]

(test/tests/time_integrators/scalar/stiff.i)

# This is a linear model problem described in Frank et al, "Order
# results for implicit Runge-Kutta methods applied to stiff systems",
# SIAM J. Numerical Analysis, vol. 22, no. 3, 1985, pp. 515-534.
#
# Problems "PL" and "PNL" from page 527 of the paper:
# { dy1/dt = lambda*y1 + y2**p, y1(0) = -1/(lambda+p)
# { dy2/dt = -y2,               y2(0) = 1
#
# The exact solution is:
# y1 = -exp(-p*t)/(lambda+p)
# y2 = exp(-t)
#
# According to the following paragraph from the reference above, the
# p=1 version of this problem should not exhibit order reductions
# regardless of stiffness, while the nonlinear version (p>=2) will
# exhibit order reductions down to the "stage order" of the method for
# lambda large, negative.

# Use Dollar Bracket Expressions (DBEs) to set the value of LAMBDA in
# a single place.  You can also set this on the command line with
# e.g. LAMBDA=-4, but note that this does not seem to override the
# value set in the input file.  This is a bit different from the way
# that command line values normally work...
# Note that LAMBDA == Y2_EXPONENT is not allowed!
# LAMBDA = -10
# Y2_EXPONENT = 2

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 1
  ny = 1
  elem_type = QUAD4
[]

[Variables]
  [./y1]
    family = SCALAR
    order = FIRST
  [../]
  [./y2]
    family = SCALAR
    order = FIRST
  [../]
[]

[ICs]
  [./y1_init]
    type = FunctionScalarIC
    variable = y1
    function = y1_exact
  [../]
  [./y2_init]
    type = FunctionScalarIC
    variable = y2
    function = y2_exact
  [../]
[]

[ScalarKernels]
  [./y1_time]
    type = ODETimeDerivative
    variable = y1
  [../]
  [./y1_space]
    type = ParsedODEKernel
    variable = y1
    function = '-(${LAMBDA})*y1 - y2^${Y2_EXPONENT}'
    args = 'y2'
  [../]
  [./y2_time]
    type = ODETimeDerivative
    variable = y2
  [../]
  [./y2_space]
    type = ParsedODEKernel
    variable = y2
    function = 'y2'
  [../]
[]

[Executioner]
  type = Transient
  [./TimeIntegrator]
    type = LStableDirk2
  [../]
  start_time = 0
  end_time = 1
  dt = 0.125
  solve_type = 'PJFNK'
  nl_max_its = 6
  nl_abs_tol = 1.e-13
  nl_rel_tol = 1.e-32 # Force nl_abs_tol to be used.
  line_search = 'none'
[]

[Functions]
  [./y1_exact]
    type = ParsedFunction
    value = '-exp(-${Y2_EXPONENT}*t)/(lambda+${Y2_EXPONENT})'
    vars = 'lambda'
    vals = ${LAMBDA}
  [../]
  [./y2_exact]
    type = ParsedFunction
    value = exp(-t)
  [../]
[]

[Postprocessors]
  [./error_y1]
    type = ScalarL2Error
    variable = y1
    function = y1_exact
    execute_on = 'initial timestep_end'
  [../]
  [./error_y2]
    type = ScalarL2Error
    variable = y2
    function = y2_exact
    execute_on = 'initial timestep_end'
  [../]
  [./max_error_y1]
    # Estimate ||e_1||_{\infty}
    type = TimeExtremeValue
    value_type = max
    postprocessor = error_y1
    execute_on = 'initial timestep_end'
  [../]
  [./max_error_y2]
    # Estimate ||e_2||_{\infty}
    type = TimeExtremeValue
    value_type = max
    postprocessor = error_y2
    execute_on = 'initial timestep_end'
  [../]
  [./value_y1]
    type = ScalarVariable
    variable = y1
    execute_on = 'initial timestep_end'
  [../]
  [./value_y2]
    type = ScalarVariable
    variable = y2
    execute_on = 'initial timestep_end'
  [../]
  [./value_y1_abs_max]
    type = TimeExtremeValue
    value_type = abs_max
    postprocessor = value_y1
    execute_on = 'initial timestep_end'
  [../]
  [./value_y2_abs_max]
    type = TimeExtremeValue
    value_type = abs_max
    postprocessor = value_y2
    execute_on = 'initial timestep_end'
  [../]
[]

[Outputs]
  csv = true
[]

(modules/tensor_mechanics/test/tests/global_strain/global_strain_hydrostat.i)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 1
    ny = 1
    nz = 1
  []
  [cnode]
    type = ExtraNodesetGenerator
    coord = '0.0 0.0 0.0'
    new_boundary = 100
    input = generated_mesh
  []
[]

[Variables]
  [./u_x]
  [../]
  [./u_y]
  [../]
  [./u_z]
  [../]
  [./global_strain]
    order = SIXTH
    family = SCALAR
  [../]
[]

[AuxVariables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./disp_z]
  [../]
[]

[AuxKernels]
  [./disp_x]
    type = GlobalDisplacementAux
    variable = disp_x
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 1
  [../]
  [./disp_y]
    type = GlobalDisplacementAux
    variable = disp_y
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 1
  [../]
  [./disp_z]
    type = GlobalDisplacementAux
    variable = disp_z
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 2
  [../]
[]

[GlobalParams]
  displacements = 'u_x u_y u_z'
  block = 0
[]

[Kernels]
  [./TensorMechanics]
  [../]
[]

[ScalarKernels]
  [./global_strain]
    type = GlobalStrain
    variable = global_strain
    global_strain_uo = global_strain_uo
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      auto_direction = 'x y z'
      variable = ' u_x u_y u_z'
    [../]
  [../]

  # fix center point location
  [./centerfix_x]
    type = DirichletBC
    boundary = 100
    variable = u_x
    value = 0
  [../]
  [./centerfix_y]
    type = DirichletBC
    boundary = 100
    variable = u_y
    value = 0
  [../]
  [./centerfix_z]
    type = DirichletBC
    boundary = 100
    variable = u_z
    value = 0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeElasticityTensor
    block = 0
    C_ijkl = '70e9 0.33'
    fill_method = symmetric_isotropic_E_nu
  [../]
  [./strain]
    type = ComputeSmallStrain
    global_strain = global_strain
  [../]
  [./global_strain]
    type = ComputeGlobalStrain
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
  [../]
  [./stress]
    type = ComputeLinearElasticStress
  [../]
[]

[UserObjects]
  [./global_strain_uo]
    type = GlobalStrainUserObject
    applied_stress_tensor = '-5e9 -5e9 -5e9 0 0 0'
    execute_on = 'Initial Linear Nonlinear'
  [../]
[]

[Postprocessors]
  [./l2err]
    type = ScalarL2Error
    variable = global_strain
    function = -0.02428571 #strain = E*(1-2*nu)/sigma
  [../]
[]

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

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = 'PJFNK'

  line_search = basic

  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm         31   preonly   lu      1'

  l_max_its = 30
  nl_max_its = 12

  l_tol = 1.0e-4

  nl_rel_tol = 1.0e-8
  nl_abs_tol = 1.0e-10

  start_time = 0.0
  num_steps = 2
[]

[Outputs]
  exodus = true
[]

(test/tests/kernels/ode/parsedode_sys_impl_test.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 2
  ny = 2
  elem_type = QUAD4
[]

[Functions]
  [./f_fn]
    type = ParsedFunction
    value = -4
  [../]
  [./bc_all_fn]
    type = ParsedFunction
    value = x*x+y*y
  [../]

  # ODEs
  [./exact_x_fn]
    type = ParsedFunction
    value = (-1/3)*exp(-t)+(4/3)*exp(5*t)
  [../]
[]

# NL

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

  # ODE variables
  [./x]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
  [./y]
    family = SCALAR
    order = FIRST
    initial_condition = 2
  [../]
[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = u
  [../]
  [./diff]
    type = Diffusion
    variable = u
  [../]
  [./uff]
    type = BodyForce
    variable = u
    function = f_fn
  [../]
[]

[ScalarKernels]
  [./td1]
    type = ODETimeDerivative
    variable = x
  [../]
  [./ode1]
    type = ParsedODEKernel
    function = '-3*x - 2*y'
    variable = x
    args = y
  [../]

  [./td2]
    type = ODETimeDerivative
    variable = y
  [../]
  [./ode2]
    type = ParsedODEKernel
    function = '-4*x - y'
    variable = y
    args = x
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = '0 1 2 3'
    function = bc_all_fn
  [../]
[]

[Postprocessors]
  active = 'exact_x l2err_x x y'

  [./x]
    type = ScalarVariable
    variable = x
    execute_on = 'initial timestep_end'
  [../]
  [./y]
    type = ScalarVariable
    variable = y
    execute_on = 'initial timestep_end'
  [../]

  [./exact_x]
    type = FunctionValuePostprocessor
    function = exact_x_fn
    execute_on = 'initial timestep_end'
    point = '0 0 0'
  [../]

  [./l2err_x]
    type = ScalarL2Error
    variable = x
    function = exact_x_fn
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  start_time = 0
  dt = 0.01
  num_steps = 100

  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = ode_sys_impl_test_out
  exodus = true
[]

(examples/ex18_scalar_kernel/ex18.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 10
  ny = 10
  elem_type = QUAD4
[]

[Functions]
  # ODEs
  [./exact_x_fn]
    type = ParsedFunction
    value = (-1/3)*exp(-t)+(4/3)*exp(5*t)
  [../]
  [./exact_y_fn]
    type = ParsedFunction
    value = (2/3)*exp(-t)+(4/3)*exp(5*t)
  [../]
[]

[Variables]
  [./diffused]
    order = FIRST
    family = LAGRANGE
  [../]

  # ODE variables
  [./x]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
  [./y]
    family = SCALAR
    order = FIRST
    initial_condition = 2
  [../]

[]

[Kernels]
  [./td]
    type = TimeDerivative
    variable = diffused
  [../]
  [./diff]
    type = Diffusion
    variable = diffused
  [../]
[]

[ScalarKernels]
  [./td1]
    type = ODETimeDerivative
    variable = x
  [../]
  [./ode1]
    type = ImplicitODEx
    variable = x
    y = y
  [../]

  [./td2]
    type = ODETimeDerivative
    variable = y
  [../]
  [./ode2]
    type = ImplicitODEy
    variable = y
    x = x
  [../]
[]


[BCs]
  [./right]
    type = ScalarDirichletBC
    variable = diffused
    boundary = 1
    scalar_var = x
  [../]

  [./left]
    type = ScalarDirichletBC
    variable = diffused
    boundary = 3
    scalar_var = y
  [../]
[]

[Postprocessors]
  # to print the values of x, y into a file so we can plot it
  [./x]
    type = ScalarVariable
    variable = x
    execute_on = timestep_end
  [../]

  [./y]
    type = ScalarVariable
    variable = y
    execute_on = timestep_end
  [../]

  [./exact_x]
    type = FunctionValuePostprocessor
    function = exact_x_fn
    execute_on = timestep_end
    point = '0 0 0'
  [../]

  [./exact_y]
    type = FunctionValuePostprocessor
    function = exact_y_fn
    execute_on = timestep_end
    point = '0 0 0'
  [../]

  # Measure the error in ODE solution for 'x'.
  [./l2err_x]
    type = ScalarL2Error
    variable = x
    function = exact_x_fn
  [../]

  # Measure the error in ODE solution for 'y'.
  [./l2err_y]
    type = ScalarL2Error
    variable = y
    function = exact_y_fn
  [../]
[]


[Executioner]
  type = Transient
  start_time = 0
  dt = 0.01
  num_steps = 10

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'
[]

[Outputs]
  exodus = true
[]

(test/tests/kernels/ode/parsedode_pp_test.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 2
  ny = 2
  elem_type = QUAD4
[]

[Variables]
  [./x]
    family = SCALAR
    order = FIRST
    initial_condition = 0
  [../]
[]

[ScalarKernels]
  [./dt]
    type = ODETimeDerivative
    variable = x
  [../]
  [./ode1]
    type = ParsedODEKernel
    function = '-mytime'
    postprocessors = mytime
    variable = x
  [../]
[]

[Postprocessors]
  [./computed_x]
    type = ScalarVariable
    variable = x
    execute_on = 'initial timestep_end'
  [../]

  [./mytime]
    type = FunctionValuePostprocessor
    function = t
    execute_on = 'initial timestep_begin'
  [../]

  [./exact_x]
    type = FunctionValuePostprocessor
    function = '0.5*t^2'
    execute_on = 'initial timestep_end'
  [../]

  [./l2err_x]
    type = ScalarL2Error
    variable = x
    function = '0.5*t^2'
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  dt = 0.1
  num_steps = 10

  solve_type = 'NEWTON'
[]

[Outputs]
  file_base = ode_pp_test_out
  hide = 'x mytime'
  csv = true
[]

(test/tests/tag/scalar_tag_vector.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 1
  ny = 1
  elem_type = QUAD4
[]

[Variables]
  [./n]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
[]

[AuxVariables]
  [./tag_vector_var1]
    family = SCALAR
    order = FIRST
  [../]
  [./tag_vector_var2]
    family = SCALAR
    order = FIRST
  [../]
  [./tag_matrix_var2]
    family = SCALAR
    order = FIRST
  [../]
[]

[ScalarKernels]
  [./dn]
    type = ODETimeDerivative
    variable = n
    extra_matrix_tags = 'mat_tag1 mat_tag2'
    extra_vector_tags = 'vec_tag1'
  [../]

  [./ode1]
    type = ParsedODEKernel
    function = '-n'
    variable = n
    extra_matrix_tags = 'mat_tag1'
    extra_vector_tags = 'vec_tag1'
  [../]

  [./ode2]
    type = ParsedODEKernel
    function = '-n'
    variable = n
    vector_tags = 'vec_tag2'
    matrix_tags = 'mat_tag2'
  [../]
[]

[AuxScalarKernels]
  [./TagVectorAux]
    type = ScalarTagVectorAux
    variable = tag_vector_var1
    v = n
    vector_tag  = vec_tag1
    execute_on = timestep_end
  [../]

  [./TagVectorAux2]
    type = ScalarTagVectorAux
    variable = tag_vector_var2
    v = n
    vector_tag  = vec_tag2
    execute_on = timestep_end
  [../]

  [./TagMatrixAux2]
    type = ScalarTagMatrixAux
    variable = tag_matrix_var2
    v = n
    matrix_tag  = mat_tag2
    execute_on = timestep_end
  [../]
[]

[Problem]
  type = TagTestProblem
  test_tag_vectors =  'time nontime residual vec_tag1 vec_tag2'
  test_tag_matrices = 'mat_tag1 mat_tag2'

  extra_tag_matrices = 'mat_tag1 mat_tag2'
  extra_tag_vectors  = 'vec_tag1 vec_tag2'
[]

[Executioner]
  type = Transient
  start_time = 0
  num_steps = 10
  dt = 0.001
  dtmin = 0.001 # Don't allow timestep cutting
  solve_type = NEWTON
  nl_max_its = 2
  nl_abs_tol = 1.e-12 # This is an ODE, so nl_abs_tol makes sense.
[]

[Functions]
  [./exact_solution]
    type = ParsedFunction
    value = exp(t)
  [../]
[]

[Postprocessors]
  [./error_n]
    # Post processor that computes the difference between the computed
    # and exact solutions.  For the exact solution used here, the
    # error at the final time should converge at O(dt^p), where p is
    # the order of the method.
    type = ScalarL2Error
    variable = n
    function = exact_solution
    # final is not currently supported for Postprocessor execute_on...
    # execute_on = 'final'
  [../]
[]

[Outputs]
  csv = true
[]

(test/tests/time_integrators/explicit_ssp_runge_kutta/explicit_ssp_runge_kutta.i)

# This test solves the following IVP:
#   du/dt = f(u(t), t),   u(0) = 1
#   f(u(t), t) = -u(t) + t^3 + 3t^2
# The exact solution is the following:
#   u(t) = exp(-t) + t^3

[Mesh]
  [./mesh]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 1
  [../]
[]

[Variables]
  [./u]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
[]

[ScalarKernels]
  [./time_derivative]
    type = ODETimeDerivative
    variable = u
  [../]
  [./source_part1]
    type = ParsedODEKernel
    variable = u
    function = 'u'
  [../]
  [./source_part2]
    type = PostprocessorSinkScalarKernel
    variable = u
    postprocessor = sink_pp
  [../]
[]

[Functions]
  [./sink_fn]
    type = ParsedFunction
    value = '-t^3 - 3*t^2'
  [../]
[]

[Postprocessors]
  [./sink_pp]
    type = FunctionValuePostprocessor
    function = sink_fn
    execute_on = 'LINEAR NONLINEAR'
  [../]
  [./l2_err]
    type = ScalarL2Error
    variable = u
    function = ${fparse exp(-0.5) + 0.5^3}
  [../]
[]

[Executioner]
  type = Transient

  [./TimeIntegrator]
    type = ExplicitSSPRungeKutta
    order = 1
  [../]

  end_time = 0.5
  dt = 0.1
[]

[Outputs]
  file_base = 'first_order'
  exodus = true
  [./csv]
    type = CSV
    show = 'u'
    execute_on = 'FINAL'
  [../]
[]

Input Parameters
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