Downwind Gauß-Seidel Smoothing for Convection Dominated Problems

In the case of convection dominated problems, multi-grid methods require an appropriate smoothing to ensure robustness. As a first approach we discuss a Gauß-Seidel smoothing with a correct numbering of the unknowns and if necessary a special block partitioning. Numerical experiments show that, in the case of general convection directions, the multi-grid algorithms obtained in this way have the same properties as in the model situation. If the graph arising from the convection part is acyclic, we describe a numbering algorithms which is valid for all spatial dimensions. Cycles give rise to special blocks for a blockwise Gauß-Seidel smoothing. We describe an algorithm for the two-dimensional case. The proposed algorithms require a computational work of optimal order (linear in the size of the problem).