From a370b06306715c479a1f5afdaac3f075aa5f932d Mon Sep 17 00:00:00 2001 From: Luca Heltai Date: Thu, 30 Apr 2020 14:09:08 +0200 Subject: [PATCH] Try to fix doxygen. --- examples/step-70/doc/builds-on | 2 +- examples/step-70/doc/intro.dox | 11 +++++------ 2 files changed, 6 insertions(+), 7 deletions(-) diff --git a/examples/step-70/doc/builds-on b/examples/step-70/doc/builds-on index 16313b3a57..d69f25861c 100644 --- a/examples/step-70/doc/builds-on +++ b/examples/step-70/doc/builds-on @@ -1 +1 @@ -step-6, step-22, step-32, step-55, step-60 +step-6 step-22 step-32 step-55 step-60 diff --git a/examples/step-70/doc/intro.dox b/examples/step-70/doc/intro.dox index 0db56969c8..4f6443f016 100644 --- a/examples/step-70/doc/intro.dox +++ b/examples/step-70/doc/intro.dox @@ -66,7 +66,6 @@ We are going to solve the following differential problem: given a sufficiently regular function $g$ on $\Gamma$, find the solution $(\textbf{u},p)$ to @f{eqnarray*} -{ -\Delta \mathbf{u} + \nabla p &=& 0,\\ -\nabla \cdot \textbf{u} &=& 0,\\ \textbf{u} &=& \textbf{g} \text{ in } \Gamma,\\ @@ -92,7 +91,7 @@ The weak form of the Stokes equations is obtained by first writing it in vector \end{pmatrix} = \begin{pmatrix} - {0 + 0 \\ 0 \end{pmatrix}, @@ -136,7 +135,7 @@ or a surface in a three-dimensional domain. The weak imposition of the Dirichlet boundary condition on $\Gamma$ is done through Nitsche method. This is achieved by using the following modified formulation : -@f{eqnarray*}{ +@f{eqnarray*} (\nabla \textbf{v}, \nabla \textbf{u})_{\Omega} + (\nabla \cdot \textbf{v}, p)_{\Omega} + (q, \nabla \cdot \textbf{u})_{\Omega} - (\nabla\textbf{v}\cdot \textbf{n},\textbf{u})_{\Gamma} + \beta (\textbf{v}},\textbf{u})_{\Gamma} &=& -(\nabla\textbf{v}\cdot \textbf{n},\textbf{g})_{\Gamma} @@ -150,7 +149,7 @@ be consistent and stable. We note that the additional terms on the left-hand and right-hand side are equal since $\textbf{u}=\textbf{g}\text{ in } \Gamma$. It follows that : -@f{eqnarray*}{ +@f{eqnarray*} (\nabla\textbf{v}\cdot \textbf{n},\textbf{u})_{\Gamma} + \beta (\textbf{v},\textbf{u})_{\Gamma} &=& -(\nabla\textbf{v}\cdot \textbf{n},\textbf{g})_{\Gamma} + \beta (\textbf{v},\textbf{g})_{\Gamma} @@ -158,7 +157,7 @@ It follows that : We note that an alternative formulation can be used : -@f{eqnarray*}{ +@f{eqnarray*} (\nabla \textbf{v}, \nabla \textbf{u})_{\Omega} + (\nabla \cdot \textbf{v}, p)_{\Omega} + (q, \nabla \cdot \textbf{u})_{\Omega} + (\nabla \textbf{v}\cdot \textbf{n},\textbf{u})_{\Gamma} + \beta (\textbf{v},\textbf{u})_{\Gamma} &=& (\nabla \textbf{v}\cdot \textbf{n},\textbf{g})_{\Gamma} @@ -186,7 +185,7 @@ In this case, $\Gamma$ has the same dimension, but is imbedded into $\Omega$. In the case of $\mathcal{L}^2$ penalization, an additional Darcy term is added within $\Gamma$ resulting in : -@f{eqnarray*}{ +@f{eqnarray*} (\nabla \textbf{v}, \nabla \textbf{u})_{\Omega} + (\nabla \cdot \textbf{v}, p)_{\Omega} + (q, \nabla \cdot \textbf{u})_{\Omega} + \beta_1 (\textbf{v}},\textbf{u})_{\Gamma} &=& -- 2.39.5