From: Wolfgang Bangerth Date: Wed, 7 May 2008 14:26:42 +0000 (+0000) Subject: Use h3/h4 tags for headings, since higher tags are reserved for top-level headers. X-Git-Tag: v8.0.0~9181 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=dabc9679fa74bafca5bd192ec6dda960b2b6eca3;p=dealii.git Use h3/h4 tags for headings, since higher tags are reserved for top-level headers. git-svn-id: https://svn.dealii.org/trunk@16044 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/examples/step-33/doc/intro.dox b/deal.II/examples/step-33/doc/intro.dox index 316b73c0ee..97e331790d 100644 --- a/deal.II/examples/step-33/doc/intro.dox +++ b/deal.II/examples/step-33/doc/intro.dox @@ -11,7 +11,7 @@ on different meshes, with differing boundary conditions. The program also uses the Trilinos linear solvers (Aztec/Amesos) and an automatic differentiation package, Sacado, which is also part of Trilinos. -

Euler flow

+

Euler flow

The equations for a compressible, inviscid gas (the Euler equations) are a basic system of conservation laws, in spatial dimension $d$, @@ -38,7 +38,7 @@ This problem obviously falls into the class of vector-valued problem. A general overview of how to deal with these problems in deal.II can be found in the @ref vector_valued module. -

Discretization

+

Discretization

Discretization happens in the usual way, taking into account that this is a hyperbolic problem in the same style as the simple one discussed @@ -98,7 +98,7 @@ We solve the nonlinear system by a Newton iteration, i.e. by iterating until $|R(\mathbf{W}^k)|$ (the residual) is sufficiently small. -

Auto-Differentiation

+

Auto-Differentiation

Since computing the Jacobian $\partial R$ is a terrible beast, we use an automatic differentiation package, Sacado, to do this. Sacado is a package within the Trilinos solvers +

Trilinos solvers

The program uses either the Aztec iterative solvers, or the Amesos sparse direct solver, both provided by the Trilinos package. This package is inherently designed to be used in a parallel program, however, @@ -164,7 +164,7 @@ to describe the parallel distribution of a vector, and to define sparse matrices on these vectors. Please view the commented code for more details on how these solvers are used within the example. -

Adaptivity

+

Adaptivity

The example uses an ad-hoc refinement indicator that shows some usefulness in shock-type problems, and in the downhill flow example included. We refine according to the squared gradient of the density. Hanging nodes are handled by computing the numerical flux across cells that are of differing @@ -184,7 +184,7 @@ tends not to slow the simulation to a halt. This, of course, is purely a heuris if the author's advisor heard about it, the author would likely be exiled forever from the finite element error estimation community. -

Input Deck

+

Input Deck

We use an input file deck to drive the simulation. In this way, we can alter the boundary conditions and other important properties of the simulation without having to recompile. For more information on