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Add docs for the new FE family, bcs and kernels (#26105)
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framework/doc/content/source/bcs/VectorDivPenaltyDirichletBC.md
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# VectorDivPenaltyDirichletBC | ||
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!syntax description /BCs/VectorDivPenaltyDirichletBC | ||
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## Overview | ||
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`VectorDivPenaltyDirichletBC` enforces, in a weak sense, a Dirichlet boundary | ||
condition on the divergence of a nonlinear vector variable $\vec{u}$ by setting | ||
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\begin{equation} | ||
R_i(\vec{u}) = p($\vec{\psi_i}$ \cdot \hat{n}, (\vec{u} - \vec{u}_0) \cdot \hat{n}) | ||
\end{equation} | ||
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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. | ||
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## Example Input File Syntax | ||
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!listing coupled_electrostatics.i block=BCs | ||
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!syntax parameters /BCs/VectorDivPenaltyDirichletBC | ||
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!syntax inputs /BCs/VectorDivPenaltyDirichletBC | ||
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!syntax children /BCs/VectorDivPenaltyDirichletBC |
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# DivField | ||
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!syntax description /Kernels/DivField | ||
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## Overview | ||
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!style halign=left | ||
The DivField object implements the following PDE term for coupled scalar-vector | ||
PDE systems: | ||
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\begin{equation} | ||
k \nabla \cdot \vec{u}, | ||
\end{equation} | ||
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where $k$ is a constant scalar coefficient and $\vec{u}$ is a vector field | ||
variable. Given scalar test functions $\psi_i$, the weak form, in inner-product notation, is given by: | ||
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\begin{equation} | ||
R_i(\vec{u}) = (\psi_i, k \nabla \cdot \vec{u}) \quad \forall \psi_i. | ||
\end{equation} | ||
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## Example Input File Syntax | ||
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!listing coupled_electrostatics.i block=Kernels/divergence | ||
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!syntax parameters /Kernels/DivField | ||
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!syntax inputs /Kernels/DivField | ||
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!syntax children /Kernels/DivField |
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# GradField | ||
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!syntax description /Kernels/GradField | ||
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## Overview | ||
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!style halign=left | ||
The GradField object implements the following PDE term for coupled | ||
scalar-vector PDE systems: | ||
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\begin{equation} | ||
- k \nabla p, | ||
\end{equation} | ||
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where $k$ is a constant scalar coefficient and $p$ is a scalar field variable. | ||
Given vector test functions $\vec{\psi_i}$, the weak form, in inner-product | ||
notation, is given by: | ||
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\begin{equation} | ||
R_i(p) = (\nabla \cdot \vec{\psi_i}, k p) \quad \forall \vec{\psi_i}. | ||
\end{equation} | ||
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## Example Input File Syntax | ||
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!listing coupled_electrostatics.i block=Kernels/gradient | ||
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!syntax parameters /Kernels/GradField | ||
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!syntax inputs /Kernels/GradField | ||
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!syntax children /Kernels/GradField |
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