Mesh independent superlinear PCG rates via compact-equivalent operators

O. W.E. Axelssont, János Karátson

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

The subject of the paper is the mesh independent convergence of the preconditioned conjugate gradient (PCG) method for nonsymmetric elliptic problems. The approach of equivalent operators is involved, in which one uses the discretization of another suitable elliptic operator as preconditioning matrix. By introducing the notion of compact-equivalent operators, it is proved that for a wide class of elliptic problems the superlinear convergence of the obtained PCG method is mesh independent under finite element discretizations; that is, the rate of superlinear convergence is given in the form of a sequence which is mesh independent and is determined only by the elliptic operators.

Original languageEnglish
Pages (from-to)1495-1516
Number of pages22
JournalSIAM Journal on Numerical Analysis
Volume45
Issue number4
DOIs
Publication statusPublished - Dec 1 2007

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Keywords

  • Conjugate gradient method
  • Equivalent operators
  • Mesh independence
  • Nonsymmetric elliptic problems
  • Preconditioning
  • Superlinear convergence

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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