Some justification and comparison of solution method for grid approximations of convection-diffusion problem
by
Eugene D. Karepova
Institute of Computation Modelling, Krasnoyarsk, Russia

We deal with Dirichlet problem in rectangle for 2D convection- dominated convection-diffusion equation. Strongly unsymmetrical structure of its discrete analogues leads to question of reasonable selection of solution method for result algebraic system.

The convergence of Gauss-Seidel methods is studied both numerically and analytically. Pointwise Gauss-Seidel method has a bad convergence which is additionally sensitive to grid condensation in boundary layer vicinity. Blockwise Gauss-Seidel method allows to improve the convergence. The estimate of convergence in this case is reduced to an estimate of pointewise Gauss-Seidel method for ordinary differential equation. This estimate is independent of grid condensation in the vicinity of parabolic boundary layer. The main term of error for blockwise Gauss- Seidel method is estimated analytically.

The cascadic algorithm use to improve of convergence additional. Comparison is realized for difference types of grid condensations: Bakhvalov, Shishkin, Liseikin and adaptive types.

Date received: March 9, 2000