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

Michel Fournié; Samir Karaa

doi:10.1007/BF02832060

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

Michel Fournié, Samir Karaa^*

^*Corresponding author for this work

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	349-363
Number of pages	15
Journal	Journal of Applied Mathematics and Computing
Volume	22
Issue number	3
DOIs	https://doi.org/10.1007/BF02832060
Publication status	Published - Oct 2006

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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10.1007/BF02832060

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AU - Karaa, Samir

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AB - 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.

KW - compact scheme

KW - Elliptic problems

KW - iterative methods

KW - mixed derivatives

KW - multigrid method

KW - preconditioning techniques

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