From a62f49c425066a2e176efb893a3bf42bb406d3a6 Mon Sep 17 00:00:00 2001 From: Julius Witte Date: Mon, 6 Apr 2020 16:07:30 +0200 Subject: [PATCH] fix typos --- examples/step-47/doc/intro.dox | 4 ++-- examples/step-47/step-47.cc | 8 ++++---- 2 files changed, 6 insertions(+), 6 deletions(-) diff --git a/examples/step-47/doc/intro.dox b/examples/step-47/doc/intro.dox index 9991a52c10..86fab3feed 100644 --- a/examples/step-47/doc/intro.dox +++ b/examples/step-47/doc/intro.dox @@ -318,7 +318,7 @@ the following terms: \average{\frac{\partial^2 v_h}{\partial \mathbf n^2}} \jump{\frac{\partial u_h}{\partial \mathbf n}} + \sum_{e \in \mathbb{F}} - \frac{\sigma}{h_e}\int_e + \frac{\gamma}{h_e}\int_e \jump{\frac{\partial v_h}{\partial \mathbf n}} \jump{\frac{\partial u_h}{\partial \mathbf n}}. @f} @@ -508,7 +508,7 @@ As a consequence, we then need choose as boundary conditions the following: \pi\sin(\pi x) \cos(\pi y) \end{pmatrix}\right|_{\partial\Omega} \cdot \mathbf n. @f} -The right hand side is easily computes as +The right hand side is easily computed as @f{align*}{ f = \Delta^2 u = 4 \pi^4 \sin(\pi x) \sin(\pi y). @f} diff --git a/examples/step-47/step-47.cc b/examples/step-47/step-47.cc index 8fb352ab97..63c3714a35 100644 --- a/examples/step-47/step-47.cc +++ b/examples/step-47/step-47.cc @@ -491,7 +491,7 @@ namespace Step47 // In the formula above, $h_K$ is the size of cell $K$. But this // is not quite so straightforward either: If one uses highly // stretched cells, then a more involved theory says that $h$ - // should be replaced be the diameter of cell $K$ normal to the + // should be replaced by the diameter of cell $K$ normal to the // direction of the edge in question. It turns out that there // is a function in deal.II for that. Secondly, $h_K$ may be // different when viewed from the two different sides of a face. @@ -521,8 +521,8 @@ namespace Step47 // of the bilinear form were as follows: // @f{align*}{ // -\sum_{e \in \mathbb{F}} \int_{e} - // \jump{ \frac{\partial^2 v_h}{\partial \mathbf n^2}} - // \average{\frac{\partial u_h}{\partial \mathbf n}} \ ds + // \jump{ \frac{\partial v_h}{\partial \mathbf n}} + // \average{\frac{\partial^2 u_h}{\partial \mathbf n^2}} \ ds // -\sum_{e \in \mathbb{F}} \int_{e} // \average{\frac{\partial^2 v_h}{\partial \mathbf n^2}} // \jump{\frac{\partial u_h}{\partial \mathbf n}} \ ds @@ -796,7 +796,7 @@ namespace Step47 // solution $u_h$, but given the Lagrange shape functions we use, $u_h$ of // course has kinks at the interfaces between cells, and consequently second // derivatives are singular at interfaces. As a consequence, we really only - // integrating over the interiors of the cells and ignore the interface + // integrate over the interior of cells and ignore the interface // contributions. This is *not* an equivalent norm to the energy norm for // the problem, but still gives us an idea of how fast the error converges. // -- 2.39.5