Alternate overlapping schwarz method for singularly perturbed semilinear convection-diffusion problems

Abstract

We propose an alternate overlapping Schwarz method to solve the singularly perturbed semilinear convection-diffusion problems. The method decomposes the original domain into two overlapping subdomains. One, the outside boundary layer subdomain, and the other, inside boundary layer subdomain. On the outside boundary layer subdomain, a combination of the second order compact difference scheme and central difference scheme with uniform mesh is considered; while on the inside boundary layer subdomain a central difference scheme with a special piecewise-uniform mesh is considered. The convergence analysis is given and the method is shown to have almost second order parameter-uniform convergence. Numerical experiments are presented to demonstrate the efficiency of the method.