Ingo Gaertner <[email protected]> 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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