Asymptotic Stability of a 9-Point Multigrid Algorithm for the Convection-Diffusion Equations

Jules Kouatchou

Department of Mathematics
The George Washington University
Washington, DC 20052


Abstract

We consider the solution of the convection-diffusion equation in two dimension by a 9-point discretization formula combined with multigrid algorithm. We analytically prove the epsilon-asymptotic stability of the coarse-grid operators. Two strategies are examined. A method to compute the asymptotic convergence is described and applied to the multigrid algorithm.