The solution of a semilinear evolutionary convection–diffusion problem by a monotone domain decomposition algorithm

Abstract

This paper deals with a monotone domain decomposition algorithm for solving a semilinear singularly perturbed convection–diffusion problem of parabolic type. On each time level, the monotone method (known as the method of lower and upper solutions) is applied to computing a nonlinear upwind difference scheme obtained after discretization of the continuous problem. A monotone domain decomposition algorithm based on a modification of the Schwarz alternating method is constructed. The rate of convergence of the monotone algorithm is estimated. Uniform convergence properties of the monotone domain decomposition algorithm are studied. Numerical experiments are presented.