On the convergence of multigrid iterations to flow problems

Prof. Anders Szepessy

Department of Numerical Analysis and Computing Science, Royal Institute of Technology, Stockholm Sweden

I will analyze multigrid methods for solving convection equations and conservation laws obtained by the streamline diffusion finite element method. The main result proves that a V-cycle, including pre and post smoothing, damps the residual in $L_1^{loc}$ , independent of the mesh size, for a uniform mesh and a constant coefficient convection dominated convection diffusion problem. The proof is based on discrete Green's functions related to the smoothing and correction operators. The analysis confirms numerical experiments showing the dependence of the damping on the choice of artificial diffusion and the number of smoothing steps.