Robustness of multi-grid applied to anisotropic equations on convex domains and on domains with re-entrant corners

R.P. Stevenson

Research output: Contribution to journalArticleAcademicpeer-review

18 Citations (Scopus)

Abstract

We analyse multi-grid applied to anisotropic equations within the framework of smoothing and approximation-properties developed by Hack busch. For a model anisotropic equation on a square, we give an up-till-now missing proof of an estimate concerning the approximation property which is essential to show robustness. Furthermore, we show a corresponding estimate for a model anisotropic equation on an L-shaped domain. The existing estimates for the smoothing property are not suitable to prove robustness for either 2-cyclic Gauss-Seidel smoothers or for less regular problems such as our second model equation. For both cases, we give sharper estimates. By combination of our results concerning smoothing- and approximation-properties, robustness of W-cycle multi-grid applied to both our model equations will follow for a number of smoothers.
Original languageEnglish
Pages (from-to)373-398
Number of pages26
JournalNumerische Mathematik
Volume66
Issue number1
DOIs
Publication statusPublished - 1993

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