git-svn-id: https://svn.dealii.org/trunk@23127 0785d39b-7218-0410-832d-ea1e28bc413d

diff --git a/deal.II/examples/step-38/doc/intro.dox b/deal.II/examples/step-38/doc/intro.dox
index efac20be85ff289f8c5364f4877e8b07a31a1c06..5a1d33c6e9ed95324345c3d6ff6a50d1392cbf94 100644 (file)
--- 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 - \mathbf n \ D \mathbf n \ \mathbf n ).
+\Delta_S v = \Delta \tilde v - \mathbf n^T \ D^2 \tilde v \ \mathbf n - (\mathbf n \cdot \nabla \tilde v) (\nabla \cdot \mathbf n - \mathbf n^T \ D \mathbf n \ \mathbf n ).
 @f]
 Worth mentioning, the term $\nabla \cdot \mathbf n - \mathbf n \ D \mathbf n \ \mathbf n$ appearing in the above expression is the total curvature of the surface (sum of principal curvatures).
 
@@ -148,7 +148,7 @@ 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 \kappa,
+    -\Delta_\Gamma u =  \Delta u - \mathbf n^T \ D^2 u \ \mathbf n - (\mathbf n \cdot \nabla u)\ \kappa,
   @f]  
   where $\kappa$ is the total curvature of $\Gamma$.
   Since we are on the unit circle, $\mathbf n=\mathbf x$ and $\kappa = 1$ so that