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Most of my work is based on the dune-fem module which I'm developing.Here are a few example applications showing the solution to some convection dominated evolution equations.

Forward facing stepmeteorological test case../swe_river.gifmean curvature flow

Left to right: 3d Euler equations on adaptive, parallel grid, a meteorological benchmark problem based on the compressible Navier-Stokes equation, river flooding using the 2d shallow water equations. The last show surface evolution under mean curvature flow. More detailed descriptions of these problems and further examples are found on the dune-fem gallery.