From: Wolfgang Bangerth Date: Wed, 7 May 2008 14:25:42 +0000 (+0000) Subject: Use h3/h4 tags for headings, since higher tags are reserved for top-level headers. X-Git-Tag: v8.0.0~9182 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=004c30a2f2eb22d8690a40de645101646ffb6985;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@16043 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/examples/step-31/doc/intro.dox b/deal.II/examples/step-31/doc/intro.dox index 733c64d08f..18c9dbb0df 100644 --- a/deal.II/examples/step-31/doc/intro.dox +++ b/deal.II/examples/step-31/doc/intro.dox @@ -1,7 +1,7 @@

Introduction

-

The Boussinesq equations

+

The Boussinesq equations

This program deals with an interesting physical problem: how does a fluid (i.e. a liquid or gas) behave if it experiences differences in @@ -108,7 +108,7 @@ earth's interior and surface structure. -

%Boundary and initial conditions

+

%Boundary and initial conditions

Since the Boussinesq equations are derived under the assumption that inertia of the fluid's motion does not play a role, the flow field is at each time @@ -130,7 +130,7 @@ boundary, or any number of other conditions that are physically reasonable. In this program, we will use no normal flux conditions. -

Solution approach

+

Solution approach

Like the equations solved in @ref step_21 "step-21", we here have a system of differential-algebraic equations (DAE): with respect to the time @@ -158,7 +158,7 @@ although we will have to make adjustments for the change in operator in the top-left corner of the differential operator. -

Time stepping

+

Time stepping

The structure of the problem as a DAE allows us to use the same strategy as we have already used in @ref step_21 "step-21", i.e. we @@ -191,7 +191,7 @@ advection is treated explicitly using the just-computed velocity field. -

Weak form and space discretization

+

Weak form and space discretization

Like solving the mixed Laplace equations, solving the Stokes equations requires us to choose particular pairs of finite elements for @@ -264,7 +264,7 @@ divergence-free: -

Linear solvers

+

Linear solvers

As explained above, our approach to solving the joint system for velocities/pressure on the one hand and temperature on the other is to use an