Domain decomposition for an advection–diffusion problem with parabolic layers

摘要

This paper deals with multidomain domain decomposition algorithms applied to the solution of a singularly perturbed advection–diffusion problem with parabolic layers. Our purpose is to study the algorithms applied to finite difference approximations of the problem. The finite difference approximations make use of special piecewise uniform meshes. We consider two algorithms: the first one is based on decomposition of the computational domain into nonoverlapping vertical subdomains, and second uses decomposition into nonoverlapping horizontal subdomains. Convergence properties of the algorithms are established. Numerical results for a test problem are presented.