Abstract
TheMGR[v] algorithms of Ries, Trottenberg and Winter, the Algorithms 2.1 and 6.1 of Braess and the Algorithm 4.1 of Verfurth are all multigrid algorithms for the solution of the discrete Poisson equation (with Dirichlet boundary conditions) based on red-black Gauss-Seidel smoothing. Both Braess and Verfurth give explicit numerical upper bounds on the rate of convergence of their methods in convex polygonal domains. In this work we reconsider these problems and obtain improved estimates for theh?2h Algorithm 4.1 as well asW-cycle estimates for both schemes in non-convex polygonal domains. The proofs do not depend on the strengthened Cauchy inequality.
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