- variableThe name of the variable that this boundary condition applies to
C++ Type:NonlinearVariableName

Description:The name of the variable that this boundary condition applies to

- boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector

Description:The list of boundary IDs from the mesh where this boundary condition applies

# DiffusionFluxBC

Computes a boundary residual contribution consistent with the Diffusion Kernel. Does not impose a boundary condition; instead computes the boundary contribution corresponding to the current value of grad(u) and accumulates it in the residual vector.

## Description

`DiffusionFluxBC`

is a `FluxBC`

which is appropriate for use with the boundary terms arising from the `Diffusion`

`Kernel`

. `DiffusionFluxBC`

does not "enforce" a boundary condition per-se (see, e.g. `DirichletBC`

, `NeumannBC`

, and related classes for that). Instead, this class is responsible for computing the residual (and Jacobian) contributions due to the boundary contribution arising from integration by parts on the `Diffusion`

`Kernel`

.

The standard theory of elliptic operators requires the specification of boundary conditions on all parts of the boundary, so "implicitly" computing a residual contribution in this manner (instead of replacing it with the correct "data") falls outside of this theory. That said, there are instances where such an approach gives reasonable results in practice, see, for example, the paper by Griffiths (1997).

As an example, consider the Poisson problem with mixed boundary conditions: (1) where is the domain, and is its boundary, and no boundary conditions are specified on . The weak formulation of this problem is: find satisfying the Dirichlet boundary conditions and such that (2) holds for every , i.e. test functions that vanish on the Dirichlet boundary. The `DiffusionFluxBC`

class would then be used to compute the last term in Eq. (2).

## References

- D. F. Griffiths.
The `No Boundary Condition' outflow boundary condition.
*International Journal of Numerical Methods in Fluids*, 24(4):393–411, 1997. URL: http://tinyurl.com/y77au2k.[BibTeX]

## Example Input Syntax

```
[./all]
type = DiffusionFluxBC
variable = u
boundary = '2 4 100 101'
[../]
```

(test/tests/mortar/continuity-2d-conforming/equalgradient.i)## Input Parameters

- displacementsThe displacements
C++ Type:std::vector

Description:The displacements

### Optional Parameters

- enableTrueSet the enabled status of the MooseObject.
Default:True

C++ Type:bool

Description:Set the enabled status of the MooseObject.

- save_inThe name of auxiliary variables to save this BC's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector

Description:The name of auxiliary variables to save this BC's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

- 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

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.

- control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector

Description:Adds user-defined labels for accessing object parameters via control logic.

- seed0The seed for the master random number generator
Default:0

C++ Type:unsigned int

Description:The seed for the master random number generator

- diag_save_inThe name of auxiliary variables to save this BC's diagonal jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector

Description:The name of auxiliary variables to save this BC's diagonal jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

- implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True

C++ Type:bool

Description:Determines whether this object is calculated using an implicit or explicit form

### Advanced Parameters

- vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime

C++ Type:MultiMooseEnum

Description:The tag for the vectors this Kernel should fill

- extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector

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

Description:The tag for the matrices this Kernel should fill

- extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector

Description:The extra tags for the matrices this Kernel should fill

### Tagging Parameters

## Input Files

- modules/phase_field/test/tests/misc/interface_grad.i
- test/tests/mortar/continuity-2d-conforming/equalgradient.i
- modules/phase_field/examples/interfacekernels/interface_fluxbc.i
- modules/combined/examples/mortar/mortar_gradient.i