EqualValueConstraint

The EqualValueConstraint class is used to enforce continuity of a variable across a mortar interface or in a periodic boundary condition. The variable is specified using the primary_variable parameter. If the solution values to be matched are between different variables, the secondary_variable parameter can also be supplied. Lagrange multipliers are used to perform the constraint enforcement.

EqualValueConstraint enforces solution continuity between secondary and primary sides of a mortar interface using lagrange multipliers

Input Parameters

primary_boundaryThe name of the primary boundary sideset.
C++ Type:BoundaryName
Options:
Description:The name of the primary boundary sideset.
primary_subdomainThe name of the primary subdomain.
C++ Type:SubdomainName
Options:
Description:The name of the primary subdomain.
secondary_boundaryThe name of the secondary boundary sideset.
C++ Type:BoundaryName
Options:
Description:The name of the secondary boundary sideset.
secondary_subdomainThe name of the secondary subdomain.
C++ Type:SubdomainName
Options:
Description:The name of the secondary subdomain.

Required Parameters

compute_lm_residualsTrueWhether to compute Lagrange Multiplier residuals
Default:True
C++ Type:bool
Options:
Description:Whether to compute Lagrange Multiplier residuals
compute_primal_residualsTrueWhether to compute residuals for the primal variable.
Default:True
C++ Type:bool
Options:
Description:Whether to compute residuals for the primal variable.
delta0The coefficient for stabilizing terms
Default:0
C++ Type:double
Options:
Description:The coefficient for stabilizing terms
diff_primary1The diffusivity on the primary side
Default:1
C++ Type:MaterialPropertyName
Options:
Description:The diffusivity on the primary side
diff_secondary1The diffusivity on the secondary side
Default:1
C++ Type:MaterialPropertyName
Options:
Description:The diffusivity on the secondary side
periodicFalseWhether this constraint is going to be used to enforce a periodic condition. This has the effect of changing the normals vector for projection from outward to inward facing
Default:False
C++ Type:bool
Options:
Description:Whether this constraint is going to be used to enforce a periodic condition. This has the effect of changing the normals vector for projection from outward to inward facing
primary_variablePrimal variable on primary surface. If this parameter is not provided then the primary variable will be initialized to the secondary variable
C++ Type:VariableName
Options:
Description:Primal variable on primary surface. If this parameter is not provided then the primary variable will be initialized to the secondary variable
secondary_variablePrimal variable on secondary surface.
C++ Type:VariableName
Options:
Description:Primal variable on secondary surface.
variableThe name of the lagrange multiplier variable that this constraint is applied to. This parameter may not be supplied in the case of using penalty methods for example
C++ Type:NonlinearVariableName
Options:
Description:The name of the lagrange multiplier variable that this constraint is applied to. This parameter may not be supplied in the case of using penalty methods for example

Optional Parameters

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.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Options:
Description:Determines whether this object is calculated using an implicit or explicit form
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Options:
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
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

extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Options:
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Options:
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime, system
Description:The tag for the matrices this Kernel should fill
vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime, time
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

Input Files

(test/tests/mortar/periodic-value/periodic.i)
(test/tests/mortar/convergence-studies/solution-continuity/continuity.i)
(test/tests/mortar/continuity-2d-conforming/conforming-2nd-order.i)
(test/tests/mortar/continuity-2d-non-conforming/sequencing-stateful-soln-continuity.i)
(test/tests/mortar/cant-do-3d/periodic.i)
(test/tests/mortar/continuity-2d-non-conforming/soln-continuity.i)
(test/tests/mortar/continuity-2d-conforming/conforming.i)
(test/tests/mortar/continuity-2d-conforming/conforming_two_var.i)
(test/tests/mortar/continuity-2d-non-conforming/dual-soln-continuity.i)

References

(test/tests/mortar/periodic-value/periodic.i)

[Mesh]
  [file]
    type = FileMeshGenerator
    file = square.msh
  []
  [secondary]
    input = file
    type = LowerDBlockFromSidesetGenerator
    new_block_id = 11
    new_block_name = "secondary"
    sidesets = '101'
  []
  [primary]
    input = secondary
    type = LowerDBlockFromSidesetGenerator
    new_block_id = 12
    new_block_name = "primary"
    sidesets = '103'
  []
[]

[Variables]
  [u]
    order = SECOND
    block = 'domain'
  []
  [lm]
    block = 'secondary'
  []
[]

[Kernels]
  [diffusion]
    type = Diffusion
    variable = u
    block = 'domain'
  []
  [force]
    type = BodyForce
    variable = u
    block = 'domain'
  []
[]

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

[Constraints]
  [ev]
    type = EqualValueConstraint
    variable = lm
    secondary_variable = u
    primary_boundary = 103
    secondary_boundary = 101
    primary_subdomain = 12
    secondary_subdomain = 11
    periodic = true
  []
[]

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

[Executioner]
  type = Steady
  solve_type = NEWTON
[]

[Outputs]
  exodus = true
[]

(test/tests/mortar/convergence-studies/solution-continuity/continuity.i)

[Mesh]
  second_order = true
  [./left_block]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1
    ymin = 0
    ymax = 1
    nx = 2
    ny = 2
    elem_type = QUAD4
  [../]
  [./left_block_sidesets]
    type = RenameBoundaryGenerator
    input = left_block
    old_boundary_id = '0 1 2 3'
    new_boundary_name = 'lb_bottom lb_right lb_top lb_left'
  [../]
  [./left_block_id]
    type = SubdomainIDGenerator
    input = left_block_sidesets
    subdomain_id = 1
  [../]
  [./right_block]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 1
    xmax = 2
    ymin = 0
    ymax = 1
    nx = 2
    ny = 2
    elem_type = QUAD4
  [../]
  [./right_block_id]
    type = SubdomainIDGenerator
    input = right_block
    subdomain_id = 2
  [../]
  [right_block_change_boundary_id]
    type = RenameBoundaryGenerator
    input = right_block_id
    old_boundary_id = '0 1 2 3'
    new_boundary_id = '100 101 102 103'
  []
  [./combined]
    type = MeshCollectionGenerator
    inputs = 'left_block_id right_block_change_boundary_id'
  [../]
  [./block_rename]
    type = RenameBlockGenerator
    input = combined
    old_block_id = '1 2'
    new_block_name = 'left_block right_block'
  [../]
  [right_right_sideset]
    type = SideSetsAroundSubdomainGenerator
    input = block_rename
    new_boundary = rb_right
    block = right_block
    normal = '1 0 0'
  []
  [right_left_sideset]
    type = SideSetsAroundSubdomainGenerator
    input = right_right_sideset
    new_boundary = rb_left
    block = right_block
    normal = '-1 0 0'
  []
  [right_top_sideset]
    type = SideSetsAroundSubdomainGenerator
    input = right_left_sideset
    new_boundary = rb_top
    block = right_block
    normal = '0 1 0'
  []
  [right_bottom_sideset]
    type = SideSetsAroundSubdomainGenerator
    input = right_top_sideset
    new_boundary = rb_bottom
    block = right_block
    normal = '0 -1 0'
  []
  [secondary]
    input = right_bottom_sideset
    type = LowerDBlockFromSidesetGenerator
    sidesets = 'lb_right'
    new_block_id = '10001'
    new_block_name = 'secondary_lower'
  []
  [primary]
    input = secondary
    type = LowerDBlockFromSidesetGenerator
    sidesets = 'rb_left'
    new_block_id = '10000'
    new_block_name = 'primary_lower'
  []
[]

[Variables]
  [./T]
    block = 'left_block right_block'
    order = SECOND
  [../]
  [./lambda]
    block = 'secondary_lower'
  [../]
[]

[BCs]
  [./neumann]
    type = FunctionGradientNeumannBC
    exact_solution = exact_soln_primal
    variable = T
    boundary = 'lb_bottom lb_top lb_left rb_bottom rb_right rb_top'
  [../]
[]

[Kernels]
  [./conduction]
    type = Diffusion
    variable = T
    block = 'left_block right_block'
  [../]
  [./sink]
    type = Reaction
    variable = T
    block = 'left_block right_block'
  [../]
  [./forcing_function]
    type = BodyForce
    variable = T
    function = forcing_function
    block = 'left_block right_block'
  [../]
[]

[Functions]
  [./forcing_function]
    type = ParsedFunction
    value = ''
  [../]
  [./exact_soln_primal]
    type = ParsedFunction
    value = ''
  [../]
  [exact_soln_lambda]
    type = ParsedFunction
    value = ''
  []
[]

[Debug]
  show_var_residual_norms = 1
[]

[Constraints]
  [./mortar]
    type = EqualValueConstraint
    primary_boundary = rb_left
    secondary_boundary = lb_right
    primary_subdomain = primary_lower
    secondary_subdomain = secondary_lower
    secondary_variable = T
    variable = lambda
    delta = 0.4
  [../]
[]

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

[Executioner]
  solve_type = NEWTON
  type = Steady
  petsc_options = '-snes_converged_reason -ksp_converged_reason'
  petsc_options_iname = '-pc_type -snes_linesearch_type -pc_factor_mat_solver_type'
  petsc_options_value = 'lu       basic                 mumps'
[]

[Outputs]
  exodus = true
  csv = true
  [dofmap]
    type = DOFMap
    execute_on = 'initial'
  []
[]

[Postprocessors]
  [L2lambda]
    type = ElementL2Error
    variable = lambda
    function = exact_soln_lambda
    execute_on = 'timestep_end'
    block = 'secondary_lower'
  []
  [L2u]
    type = ElementL2Error
    variable = T
    function = exact_soln_primal
    execute_on = 'timestep_end'
    block = 'left_block right_block'
  []
  [h]
    type = AverageElementSize
    block = 'left_block right_block'
  []
[]

(test/tests/mortar/continuity-2d-conforming/conforming-2nd-order.i)

[Mesh]
  [file]
    type = FileMeshGenerator
    file = 2blk-conf-2nd.e
  []
  [secondary]
    input = file
    type = LowerDBlockFromSidesetGenerator
    sidesets = '101'
    new_block_id = '10001'
    new_block_name = 'secondary_lower'
  []
  [primary]
    input = secondary
    type = LowerDBlockFromSidesetGenerator
    sidesets = '100'
    new_block_id = '10000'
    new_block_name = 'primary_lower'
  []
[]

[Problem]
  kernel_coverage_check = false
[]

[Functions]
  [./exact_sln]
    type = ParsedFunction
    value = x*x+y*y
  [../]
  [./ffn]
    type = ParsedFunction
    value = -4
  [../]
[]

[Variables]
  [./u]
    order = SECOND
    family = LAGRANGE
    block = '1 2'
  [../]

  [./lm]
    order = SECOND
    family = LAGRANGE
    block = secondary_lower
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
  [./ffn]
    type = BodyForce
    variable = u
    function = ffn
  [../]
[]

[Constraints]
  [./ced]
    type = EqualValueConstraint
    variable = lm
    secondary_variable = u
    primary_boundary = 100
    primary_subdomain = 10000
    secondary_boundary = 101
    secondary_subdomain = 10001
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = '1 2 3 4'
    function = exact_sln
  [../]
[]

[Postprocessors]
  [./l2_error]
    type = ElementL2Error
    variable = u
    function = exact_sln
    block = '1 2'
    execute_on = 'initial timestep_end'
  [../]
[]

[Preconditioning]
  [./fmp]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Steady
  nl_rel_tol = 1e-14
  l_tol = 1e-14
[]

[Outputs]
  exodus = true
[]

(test/tests/mortar/continuity-2d-non-conforming/sequencing-stateful-soln-continuity.i)

[Mesh]
  second_order = true
  [file]
    type = FileMeshGenerator
    file = nodal_normals_test_offset_nonmatching_gap.e
  []
  [./primary]
    input = file
    type = LowerDBlockFromSidesetGenerator
    sidesets = '2'
    new_block_id = '20'
  [../]
  [./secondary]
    input = primary
    type = LowerDBlockFromSidesetGenerator
    sidesets = '1'
    new_block_id = '10'
  [../]
[]

[Variables]
  [./T]
    block = '1 2'
    order = SECOND
  [../]
  [./lambda]
    block = '10'
  [../]
[]

[AuxVariables]
  [ssm]
    order = CONSTANT
    family = MONOMIAL
    block = '1 2'
  []
[]

[BCs]
  [./neumann]
    type = FunctionGradientNeumannBC
    exact_solution = exact_soln
    variable = T
    boundary = '3 4 5 6 7 8'
  [../]
[]

[Kernels]
  [./conduction]
    type = Diffusion
    variable = T
    block = '1 2'
  [../]
  [./sink]
    type = Reaction
    variable = T
    block = '1 2'
  [../]
  [./forcing_function]
    type = BodyForce
    variable = T
    function = forcing_function
    block = '1 2'
  [../]
[]

[AuxKernels]
  [ssm]
    type = MaterialRealAux
    variable = ssm
    property = diffusivity
    block = '1 2'
  []
[]

[Materials]
  [./ssm]
    type = SpatialStatefulMaterial
    block = '1 2'
  [../]
[]

[Functions]
  [./forcing_function]
    type = ParsedFunction
    value = '-4 + x^2 + y^2'
  [../]
  [./exact_soln]
    type = ParsedFunction
    value = 'x^2 + y^2'
  [../]
[]

[Debug]
  show_var_residual_norms = 1
[]

[Constraints]
  [./mortar]
    type = EqualValueConstraint
    primary_boundary = 2
    secondary_boundary = 1
    primary_subdomain = 20
    secondary_subdomain = 10
    variable = lambda
    secondary_variable = T
  [../]
[]

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

[Executioner]
  solve_type = NEWTON
  type = Steady
  nl_abs_tol = 1e-12
  petsc_options_iname = '-pc_type -snes_linesearch_type -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu       basic                 NONZERO               1e-15'
  num_grids = 2
[]

[Outputs]
  exodus = true
[]

[Adaptivity]
  steps = 1
  marker = uniform
  [Markers]
    [uniform]
      type = UniformMarker
      mark = refine
    []
  []
[]

(test/tests/mortar/cant-do-3d/periodic.i)

[Mesh]
  [file]
    type = FileMeshGenerator
    file = flow_test.e
  []
  [secondary]
    input = file
    type = LowerDBlockFromSidesetGenerator
    new_block_id = 11
    new_block_name = "secondary"
    sidesets = '1'
  []
  [primary]
    input = secondary
    type = LowerDBlockFromSidesetGenerator
    new_block_id = 12
    new_block_name = "primary"
    sidesets = '2'
  []
[]

[Variables]
  [u]
    block = 'bottom middle top'
  []
  [lm]
    block = 'secondary'
  []
[]

[Kernels]
  [diffusion]
    type = Diffusion
    variable = u
    block = 'bottom middle top'
  []
  [force]
    type = BodyForce
    variable = u
    block = 'bottom middle top'
  []
[]

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

[Constraints]
  [ev]
    type = EqualValueConstraint
    variable = lm
    secondary_variable = u
    primary_boundary = top
    secondary_boundary = bottom
    primary_subdomain = 12
    secondary_subdomain = 11

    periodic = true
  []
[]

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

[Executioner]
  type = Steady
  solve_type = NEWTON
[]

[Outputs]
  exodus = true
[]

(test/tests/mortar/continuity-2d-non-conforming/soln-continuity.i)

[Mesh]
  second_order = true
  [file]
    type = FileMeshGenerator
    file = nodal_normals_test_offset_nonmatching_gap.e
  []
  [./primary]
    input = file
    type = LowerDBlockFromSidesetGenerator
    sidesets = '2'
    new_block_id = '20'
  [../]
  [./secondary]
    input = primary
    type = LowerDBlockFromSidesetGenerator
    sidesets = '1'
    new_block_id = '10'
  [../]
[]

[Problem]
  kernel_coverage_check = false
[]

[Variables]
  [./T]
    block = '1 2'
    order = SECOND
  [../]
  [./lambda]
    block = '10'
  [../]
[]

[BCs]
  [./neumann]
    type = FunctionGradientNeumannBC
    exact_solution = exact_soln
    variable = T
    boundary = '3 4 5 6 7 8'
  [../]
[]

[Kernels]
  [./conduction]
    type = Diffusion
    variable = T
    block = '1 2'
  [../]
  [./sink]
    type = Reaction
    variable = T
    block = '1 2'
  [../]
  [./forcing_function]
    type = BodyForce
    variable = T
    function = forcing_function
    block = '1 2'
  [../]
[]

[Functions]
  [./forcing_function]
    type = ParsedFunction
    value = '-4 + x^2 + y^2'
  [../]
  [./exact_soln]
    type = ParsedFunction
    value = 'x^2 + y^2'
  [../]
[]

[Debug]
  show_var_residual_norms = 1
[]

[Constraints]
  [./mortar]
    type = EqualValueConstraint
    primary_boundary = 2
    secondary_boundary = 1
    primary_subdomain = 20
    secondary_subdomain = 10
    variable = lambda
    secondary_variable = T
  [../]
[]

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

[Executioner]
  solve_type = NEWTON
  type = Steady
  petsc_options_iname = '-pc_type -snes_linesearch_type -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu       basic                 NONZERO               1e-15'
[]

[Outputs]
  exodus = true
  [dofmap]
    type = DOFMap
    execute_on = 'initial'
  []
[]

(test/tests/mortar/continuity-2d-conforming/conforming.i)

[Mesh]
  [file]
    type = FileMeshGenerator
    file = 2blk-conf.e
  []
  [secondary]
    input = file
    type = LowerDBlockFromSidesetGenerator
    sidesets = '101'
    new_block_id = '10001'
    new_block_name = 'secondary_lower'
  []
  [primary]
    input = secondary
    type = LowerDBlockFromSidesetGenerator
    sidesets = '100'
    new_block_id = '10000'
    new_block_name = 'primary_lower'
  []
[]

[Functions]
  [./exact_sln]
    type = ParsedFunction
    value = y
  [../]
  [./ffn]
    type = ParsedFunction
    value = 0
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
    block = '1 2'
  [../]

  [./lm]
    order = FIRST
    family = LAGRANGE
    block = 'secondary_lower'
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]
  [./ffn]
    type = BodyForce
    variable = u
    function = ffn
  [../]
[]

[Constraints]
  [./ced]
    type = EqualValueConstraint
    variable = lm
    secondary_variable = u
    primary_boundary = 100
    primary_subdomain = 10000
    secondary_boundary = 101
    secondary_subdomain = 10001
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = '1 2 3 4'
    function = exact_sln
  [../]
[]

[Postprocessors]
  [./l2_error]
    type = ElementL2Error
    variable = u
    function = exact_sln
    block = '1 2'
    execute_on = 'initial timestep_end'
  [../]
[]

[Preconditioning]
  [./fmp]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Steady
  nl_rel_tol = 1e-11
  l_tol = 1e-10
[]

[Outputs]
  exodus = true
[]

(test/tests/mortar/continuity-2d-conforming/conforming_two_var.i)

[Mesh]
  [file]
    type = FileMeshGenerator
    file = 2blk-conf.e
  []
  [secondary]
    input = file
    type = LowerDBlockFromSidesetGenerator
    sidesets = '101'
    new_block_id = '10001'
    new_block_name = 'secondary_lower'
  []
  [primary]
    input = secondary
    type = LowerDBlockFromSidesetGenerator
    sidesets = '100'
    new_block_id = '10000'
    new_block_name = 'primary_lower'
  []
[]

[Functions]
  [./exact_sln]
    type = ParsedFunction
    value = y
  [../]
  [./ffn]
    type = ParsedFunction
    value = 0
  [../]
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
    block = '1 2'
  [../]

  [./lm_u]
    order = FIRST
    family = LAGRANGE
    block = 'secondary_lower'
  [../]

  [./v]
    order = FIRST
    family = LAGRANGE
    block = '1 2'
  [../]

  [./lm_v]
    order = FIRST
    family = LAGRANGE
    block = 'secondary_lower'
  [../]

[]

[Kernels]
  [./diff_u]
    type = Diffusion
    variable = u
  [../]
  [./ffn]
    type = BodyForce
    variable = u
    function = ffn
  [../]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]
  [./coupled_u]
    type = CoupledForce
    variable = v
    v = u
  [../]
[]

[Constraints]
  [./ced_u]
    type = EqualValueConstraint
    variable = lm_u
    secondary_variable = u
    primary_boundary = 100
    primary_subdomain = 10000
    secondary_boundary = 101
    secondary_subdomain = 10001
  [../]
  [./ced_v]
    type = EqualValueConstraint
    variable = lm_v
    secondary_variable = v
    primary_boundary = 100
    primary_subdomain = 10000
    secondary_boundary = 101
    secondary_subdomain = 10001
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = u
    boundary = '1 2 3 4'
    function = exact_sln
  [../]
  [./allv]
    type = DirichletBC
    variable = v
    boundary = '1 2 3 4'
    value = 0
  [../]
[]

[Postprocessors]
  [./l2_error]
    type = ElementL2Error
    variable = u
    function = exact_sln
    block = '1 2'
    execute_on = 'initial timestep_end'
  [../]
  [./l2_v]
    type = ElementL2Norm
    variable = v
    block = '1 2'
    execute_on = 'initial timestep_end'
  [../]
[]

[Preconditioning]
  [./fmp]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Steady
  nl_rel_tol = 1e-12
  l_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

(test/tests/mortar/continuity-2d-non-conforming/dual-soln-continuity.i)

[Mesh]
  second_order = false
  [file]
    type = FileMeshGenerator
    file = nodal_normals_test_offset_nonmatching_gap.e
  []
  [./primary]
    input = file
    type = LowerDBlockFromSidesetGenerator
    sidesets = '2'
    new_block_id = '20'
  [../]
  [./secondary]
    input = primary
    type = LowerDBlockFromSidesetGenerator
    sidesets = '1'
    new_block_id = '10'
  [../]
[]

[Problem]
  kernel_coverage_check = false
[]

[Variables]
  [./T]
    block = '1 2'
    order = FIRST
  [../]
  [./lambda]
    block = '10'
    order = FIRST
    use_dual = true
  [../]
[]

[BCs]
  [./neumann]
    type = FunctionGradientNeumannBC
    exact_solution = exact_soln
    variable = T
    boundary = '3 4 5 6 7 8'
  [../]
[]

[Kernels]
  [./conduction]
    type = Diffusion
    variable = T
    block = '1 2'
  [../]
  [./sink]
    type = Reaction
    variable = T
    block = '1 2'
  [../]
  [./forcing_function]
    type = BodyForce
    variable = T
    function = forcing_function
    block = '1 2'
  [../]
[]

[Functions]
  [./forcing_function]
    type = ParsedFunction
    value = '-4 + x^2 + y^2'
  [../]
  [./exact_soln]
    type = ParsedFunction
    value = 'x^2 + y^2'
  [../]
[]

[Debug]
  show_var_residual_norms = 1
[]

[Constraints]
  [./mortar]
    type = EqualValueConstraint
    primary_boundary = 2
    secondary_boundary = 1
    primary_subdomain = 20
    secondary_subdomain = 10
    variable = lambda
    secondary_variable = T
  [../]
[]

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

[Executioner]
  solve_type = NEWTON
  type = Steady
  petsc_options_iname = '-pc_type -snes_linesearch_type -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu       basic                 NONZERO               1e-15'
[]

[Outputs]
  exodus = true
  [dofmap]
    type = DOFMap
    execute_on = 'initial'
  []
[]

Input Parameters
Input Files
References

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