# 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 language English 349-363 15 Journal of Applied Mathematics and Computing 22 3 https://doi.org/10.1007/BF02832060 Published - Oct 2006

### Fingerprint

High-order Schemes
Iterative methods
Difference Scheme
Elliptic Problems
Derivatives
Central Difference Schemes
GMRES Method
Iteration
Gauss-Seidel Method
Compact Scheme
Derivative
Multigrid Method
Finite Difference Scheme
Linear systems
Fourth Order
Experimental Study
Linear Systems
Numerical Solution
Coefficient

### Keywords

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

### ASJC Scopus subject areas

• Applied Mathematics
• Computational Mathematics

### Cite this

In: Journal of Applied Mathematics and Computing, Vol. 22, No. 3, 10.2006, p. 349-363.

Research output: Contribution to journalArticle

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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.

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