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

Research output: Contribution to journalArticle

18 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)291-306
Number of pages16
JournalNumerical Linear Algebra with Applications
Volume15
Issue number2-3 SPEC. ISS.
DOIs
StatePublished - Mar 1 2008

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Corner Singularity
Graded Meshes
Poisson equation
Uniform convergence
Poisson's equation
Cycle
Sobolev spaces
Gauss-Seidel
Linear Interpolation
Weighted Sobolev Spaces
Finite Element Discretization
Piecewise Linear
Jacobi
Linear systems
Optimality
Interpolation
Linear Systems
Numerical Experiment
Projection
Decomposition

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Applied Mathematics

Cite this

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Uniform convergence of the multigrid V -cycle on graded meshes for corner singularities. / Brannick, James J.; Li, Hengguang; Zikatanov, Ludmil T.

In: Numerical Linear Algebra with Applications, Vol. 15, No. 2-3 SPEC. ISS., 01.03.2008, p. 291-306.

Research output: Contribution to journalArticle

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