On maximum norm convergence of multigrid methods for elliptic boundary value problems

A.A. Reusken

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Abstract

Multigrid methods applied to standard linear finite element discretizations of linear elliptic boundary value problems in two dimensions are considered. In the multigrid method, damped Jacobi or damped Gauss-Seidel is used as a smoother. It is proven that the two-grid method with v pre-smoothing interations has a contraction number with respect to the maximum norm that is (asymptotically) bounded by Cv-1/2|lnhk|2, with hk a suitable mesh size parameter. Moreover, it is shown that this bound is sharp in the sense that a factor |ln hk| is necessary.
Original languageEnglish
Pages (from-to)378-392
Number of pages15
JournalSIAM Journal on Numerical Analysis
Volume31
Issue number2
DOIs
Publication statusPublished - 1994

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