A flow-aligning algorithm for convection-dominated problems

This paper proposes and studies an algorithm for aligning a triangulation with a given convection eld. Ap- proximate solutions of convection-dominated problems on ow-aligned meshes typically have sharper internal layers, less over and undershooting and higher accuracy. The algorithm we present can be imported easily into any 2D nite element solver, does not change the number of meshpoints, and can improve solution quality quite dramatically. This improvement in solution quality on the ow-aligned triangulation is illustrated for both the usual Galerkin method and the streamline-di usion method.