conductivity and a time scale of relevance to affect the evolution of the
earth's interior and surface structure.
+@note If you are interested in using the program as the basis for your own
+experiments, you will also want to take a look at its continuation in
+step-32. Furthermore, step-32 later was developed into the much larger open
+source code Aspect (see http://aspect.dealii.org/ ) that can solve realistic
+problems and that you may want to investigate before trying to morph step-31
+into something that can solve whatever you want to solve.
<h3>%Boundary and initial conditions</h3>
if we state the CFL condition as the requirement that the time step be
small enough so that the distance transport advects in each time step
is no longer than one <i>grid point</i> away (which for $Q_1$ elements
-is $h_K$, but for $Q_2$ elements is $h_K/2$). It turns out that $\beta$
+is $h_K$, but for $Q_2$ elements is $h_K/2$). It turns out that $\beta$
needs to be slightly larger for obtaining stable results also late in
the simulation at times larger than 60, so we actually choose it as
$\beta = 0.034$ in the code.
is, of course, to make it faster and/or increase the resolution of the
program, in particular in 3d. This is the topic of the step-32
tutorial program which will implement strategies to solve this problem in
-%parallel on a cluster.
+%parallel on a cluster. It is also the basis of the much larger open
+source code Aspect (see http://aspect.dealii.org/ ) that can solve realistic
+problems and that constitutes the further development of step-32.
Another direction would be to make the fluid flow more realistic. The program
was initially written to simulate various cases simulating the convection of