Uniform convergence of the multigrid V-cycle on graded meshes for corner singularities

This paper analyzes a multigrid (MG) V‐cycle scheme for solving the discretized 2D Poisson equation with corner singularities. Using weighted Sobolev spaces Kma(Ω) and a space decomposition based on elliptic projections, we prove that the MG V‐cycle with standard smoothers (Richardson, weighted Jaco...

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Bibliographic Details
Published inNumerical linear algebra with applications Vol. 15; no. 2-3; pp. 291 - 306
Main Authors Brannick, James J., Li, Hengguang, Zikatanov, Ludmil T.
Format Journal Article
LanguageEnglish
Published Chichester, UK John Wiley & Sons, Ltd 01.03.2008
Subjects
corner-like singularities
graded meshes
multigrid methods
uniform convergence
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Summary:This paper analyzes a multigrid (MG) V‐cycle scheme for solving the discretized 2D Poisson equation with corner singularities. Using weighted Sobolev spaces Kma(Ω) and a space decomposition based on elliptic projections, we prove that the MG V‐cycle with standard smoothers (Richardson, weighted Jacobi, Gauss–Seidel, etc.) and piecewise linear interpolation converges uniformly for the linear systems obtained by finite element discretization of the Poisson equation on graded meshes. In addition, we provide numerical experiments to demonstrate the optimality of the proposed approach. Copyright © 2008 John Wiley & Sons, Ltd.
Bibliography:istex:3EEEB2DDAC5265A13FB5EFE040BA3816AE820457
NSF - No. DMS-0555831; No. DMS-058110
Lawrence Livermore National Lab - No. B568399
ark:/67375/WNG-CN4D45NC-P
ArticleID:NLA574
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1070-5325
1099-1506
DOI:10.1002/nla.574