From 0a3c786eec64c8104cbe60c32c05e3d752369170 Mon Sep 17 00:00:00 2001 From: bonito Date: Tue, 4 Jan 2011 15:43:01 +0000 Subject: [PATCH] git-svn-id: https://svn.dealii.org/trunk@23122 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-38/doc/intro.dox | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/deal.II/examples/step-38/doc/intro.dox b/deal.II/examples/step-38/doc/intro.dox index 939cab5a41..308df9ee92 100644 --- a/deal.II/examples/step-38/doc/intro.dox +++ b/deal.II/examples/step-38/doc/intro.dox @@ -53,7 +53,7 @@ where $\tilde v$ is a "smooth" extension of $v$ in a tubular neighborhood of $\G $\mathbf n$ is the normal of $\Gamma$. Since $\Delta_S = \nabla_S \cdot \nabla_S$, we deduce @f[ -\Delta_S v = \Delta \tilde v - \mathbf n^T D \tilde v \mathbf n - (\nabla \tilde v)\cdot \mathbf n (\nabla \cdot \mathbf n). +\Delta_S v = \Delta \tilde v - \mathbf n^T \ D \tilde v \ \mathbf n - (\nabla \tilde v)\cdot \mathbf n (\nabla \cdot \mathbf n). @f] As usual, we are only interested in weak solutions for which we can use $C^0$ @@ -147,7 +147,7 @@ We produce one test case for a 2d problem and another one for 3d: solution function. There are (at least) two ways to do that. The first one is to project away the normal derivative as described above using the natural extension of $u(\mathbf x)$ (still denoted by $u$) over $\mathbb R^d$, i.e. to compute @f[ - -\Delta_\Gamma u = \Delta u - \mathbf n^T D u \mathbf n - (\nabla u)\cdot \mathbf n (\nabla \cdot \mathbf n). + -\Delta_\Gamma u = \Delta u - \mathbf n^T \ D u \ \mathbf n - (\nabla u)\cdot \mathbf n (\nabla \cdot \mathbf n). @f] Since we are on the unit circle, $\mathbf n=\mathbf x$ so that @f[ -- 2.39.5