We conduct convergence analysis on some classical stationary iterative methods for solving the two-dimensional variable coefficient convection-diffusion equation discretized by a fourth-order compact difference scheme. Several conditions are formulated under which the coefficient matrix is guaranteed to be an M-matrix. We further investigate the effect of different orderings of the grid points on the performance of some stationary iterative methods, multigrid method, and preconditioned GMRES. Three sets of numerical experiments are conducted to study the convergence behaviors of these iterative methods under the influence of the flow directions, the orderings of the grid points, and the magnitude of the convection coefficients.
|Number of pages||23|
|Journal||Computers and Mathematics with Applications|
|State||Published - Aug 2002|
Bibliographical noteFunding Information:
*This author’s research was supported in part by the U.S. National Science Foundation under Grants CCR-9902022, CCR-9988165, and CCR-0092532.
- Convection-diffusion equation
- Fourth-order compact scheme
- Grid ordering
- Iterative methods
ASJC Scopus subject areas
- Modeling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics