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

James J. Brannick; Hengguang Li; Ludmil T. Zikatanov

doi:10.1002/nla.574

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

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Abstract

This paper analyzes a multigrid (MG) V-cycle scheme for solving the discretized 2D Poisson equation with corner singularities. Using weighted Sobolev spaces K^m_a(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.

Original language	English (US)
Pages (from-to)	291-306
Number of pages	16
Journal	Numerical Linear Algebra with Applications
Volume	15
Issue number	2-3 SPEC. ISS.
DOIs	https://doi.org/10.1002/nla.574
State	Published - Mar 2008

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Applied Mathematics

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10.1002/nla.574

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title = "Uniform convergence of the multigrid V -cycle on graded meshes for corner singularities",

abstract = "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.",

author = "Brannick, \{James J.\} and Hengguang Li and Zikatanov, \{Ludmil T.\}",

year = "2008",

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journal = "Numerical Linear Algebra with Applications",

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AU - Li, Hengguang

AU - Zikatanov, Ludmil T.

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Y1 - 2008/3

N2 - 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.

AB - 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.

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U2 - 10.1002/nla.574

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AN - SCOPUS:51449095708

SN - 1070-5325

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JO - Numerical Linear Algebra with Applications

JF - Numerical Linear Algebra with Applications

IS - 2-3 SPEC. ISS.

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

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