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

A.A. Reusken

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)
149 Downloads (Pure)

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

Fingerprint

Dive into the research topics of 'On maximum norm convergence of multigrid methods for elliptic boundary value problems'. Together they form a unique fingerprint.

Cite this