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 | |
| Publication status | Published - 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
Cite this
Iterative methods and high-order difference schemes for 2D elliptic problems with mixed derivative. / Fournié, Michel; Karaa, Samir.
In: Journal of Applied Mathematics and Computing, Vol. 22, No. 3, 10.2006, p. 349-363.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Iterative methods and high-order difference schemes for 2D elliptic problems with mixed derivative
AU - Fournié, Michel
AU - Karaa, Samir
PY - 2006/10
Y1 - 2006/10
N2 - 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.
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
UR - http://www.scopus.com/inward/record.url?scp=84867999862&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84867999862&partnerID=8YFLogxK
U2 - 10.1007/BF02832060
DO - 10.1007/BF02832060
M3 - Article
VL - 22
SP - 349
EP - 363
JO - Journal of Applied Mathematics and Computing
JF - Journal of Applied Mathematics and Computing
SN - 1598-5865
IS - 3
ER -