VectorDivPenaltyDirichletBC.md

VectorDivPenaltyDirichletBC

!syntax description /BCs/VectorDivPenaltyDirichletBC

Overview

VectorDivPenaltyDirichletBC enforces, in a weak sense, a Dirichlet boundary condition on the divergence of a nonlinear vector variable $\vec{u}$ by setting

\begin{equation} R_i(\vec{u}) = p($\vec{\psi_i}$ \cdot \hat{n}, (\vec{u} - \vec{u}_0) \cdot \hat{n}) \end{equation}

where $p$ is a scalar defining the penalty value, $\vec{\psi_i}$ the test functions, and $\vec{u} - \vec{u}_0$ is the vector difference between the current solution and the Dirichlet data.

Users should instead use [VectorPenaltyDirichletBC.md] or [VectorCurlPenaltyDirichletBC.md] if they wish to set a Dirichlet boundary condition via the penalty method on the vector variable itself or its curl, respectively.

Example Input File Syntax

!listing coupled_electrostatics.i block=BCs

!syntax parameters /BCs/VectorDivPenaltyDirichletBC

!syntax inputs /BCs/VectorDivPenaltyDirichletBC

!syntax children /BCs/VectorDivPenaltyDirichletBC