[petsc-users] examples of DMPlex*FVM methods

[Jed Brown]

Ingo Gaertner <ingogaertner.tus at gmail.com> writes:
> By transport equation I mean the advection-diffusion equation. This is
> always parabolic, independent of whether it is advection dominated or
> diffusion dominated. 

This is true from an analysis perspective, but nearly meaningless from
the perspective of numerical methods on finite grids.

> And the elliptic Poisson equation can be solved by making it
> timedependent and converge to steady state, again solving a parabolic
> equation. 

Yes, but also nearly meaningless because that is a tremendously
inefficient method unless you have an efficient solver for the elliptic
case, in which cas you may as well use it.

> At least this is how I learned the terms.  My impression is that
> everybody has his hammer, be it FEM or FVM, so that every problem
> looks like a nail. You can also hammer a screw into the wall if the
> wall isn't too hard.

True, but it isn't just religion, these choices depend on what you
consider to be important, and if you have the same goals, the methods
can sometimes be made to coincide.  Anyway, there are several ways of
implementing finite volume methods for elliptic problems, but if your
problems is advection-dominated (high cell Péclet number), the
discretization of advective terms will be more important.
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