Schwarz Methods for Convection-Diffusion Problems

Abstract. Various variants of Schwarz methods for a singularly perturbed two dimensional stationary convection-diffusion problem are constructed and analysed. The iteration counts, the errors in the discrete solutions and the convergence behaviour of the numerical solutions are analysed in terms of their dependence on the singular perturbation parameter of the Schwarz methods. Conditions for the methods to converge parameter uniformly and for the number of iterations to be independent of the perturbation parameter are discussed.

• Type: Conference
• Year: 2000
• Where: NAA
• Authors: H. MacMullen, Eugene O'Riordan, Grigorii I. Shishkin
• Keywords: Mathematics, NAA 2000, Perturbation Parameter, Schwarz Methods, Singular Perturbation Parameter