Robustness of multi-grid applied to anisotropic equations on convex domains and on domains with re-entrant corners
type: Item
instance of: scholarly article
title: Robustness of multi-grid applied to anisotropic equations on convex domains and on domains with re-entrant corners
zbMATH Open document ID: 0791.65090
DOI: 10.1007/BF01385703
published in: Numerische Mathematik
publication date: 1994-07-07T00:00:00Z
full work available at URL: https://eudml.org/doc/133768
review text: We analyse multigrid applied to anisotropic equations within the framework of smoothing and approximation properties developed by \textit{W. Hackbusch} [Multi-grid methods and applications (1985; Zbl 0595.65106)]. 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 multigrid applied to both our model equations will follow for a number of smoothers.
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 569197
zbMATH Keywords: second order elliptic equation
zbMATH Keywords: finite elements
zbMATH Keywords: error estimates
zbMATH Keywords: \(L\)- shaped domain
zbMATH Keywords: \(W\)-cycle multigrid
zbMATH Keywords: anisotropic equations
zbMATH Keywords: robustness
zbMATH Keywords: Gauss-Seidel smoothers
author: Rob P. Stevenson
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 569197