Multigrid and MGR[$v$] Methods for Diffusion Equations

Abstract

The MGR[$v$] Algorithm of Ries, Trottenberg and Winter with v=0 and the Algorithm 2.1 of Braess are essentially the same multigrid algorithm for the discrete poisson equation. In this report we consider the extension to the general diffusion equation. In particular, we indicate the proof of the basic result $ρ≤\frac{1}{2}(1+Kh)$, thus extending the results of Braess and Ries Trottenberg and Winter. In addition to this theoretical result we present computational results which indicate that other constant coefficient estimates carry over to this case.