Iterative methods and high-order difference schemes for 2D elliptic problems with mixed derivative

Michel Fournié, Samir Karaa

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We derive a fourth-order compact finite difference scheme for a two-dimensional elliptic problem with a mixed derivative and constant coefficients. We conduct experimental study on numerical solution of the problem discretized by the present compact scheme and the traditional second-order central difference scheme. We study the computed accuracy achieved by each scheme and the performance of the Gauss-Seidel iterative method, the preconditioned GMRES iterative method, and the multigrid method, for solving linear systems arising from the difference schemes.

Original languageEnglish
Pages (from-to)349-363
Number of pages15
JournalJournal of Applied Mathematics and Computing
Volume22
Issue number3
DOIs
Publication statusPublished - Oct 2006

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Keywords

  • compact scheme
  • Elliptic problems
  • iterative methods
  • mixed derivatives
  • multigrid method
  • preconditioning techniques

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

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