Han, Houde; Il’in, V. P.; Kellogg, R. B.; Wei, Yuan Analysis of flow directed iterations. (English) Zbl 0743.76075 J. Comput. Math. 10, No. 1, 57-76 (1992). We consider some difference approximations to the convection diffusion equation and we treat block Gauss-Seidel iterations for the solution of these problems. We study the effect of the partitioning and ordering of the unknowns on the convergence of the Gauss-Seidel iterations. We find that, for convection dominated flow problems, the spectral radius of the iteration matrix is not an appropriate indicator of the convergence properties of the method; it is better to use a norm of the iteration matrix. Also, we find that sweeping the mesh in the direction of the underlying flow enhances the convergence of the Gauss-Seidel iterations. In one dimension it is not hard to devise an algorithm to implement this idea. In two dimensions, we give a general procedure to automate the partitioning and ordering phase of the solution process. The general procedure is described using the graph of the matrix. Cited in 5 Documents MSC: 76R99 Diffusion and convection 65F10 Iterative numerical methods for linear systems Keywords:difference approximations; convection diffusion equation; block Gauss- Seidel iterations; partitioning; ordering; spectral radius; convergence; sweeping; graph of the matrix PDFBibTeX XMLCite \textit{H. Han} et al., J. Comput. Math. 10, No. 1, 57--76 (1992; Zbl 0743.76075)