Physically Motivated Domain Decomposition for Singularly Perturbed Equations

Abstract

A domain decomposition algorithm suitable for the efficient and accurate solution of a parabolic reaction-convection-diffusion equation with small parameter multiplying the diffusion term is presented. Convergence is established via maximum principle arguments. The equation arises in the modeling of laminar transonic flow. Decomposition into subdomains is accomplished via singular perturbation analysis which dictates regions where certain reduced equations may be solved in place of the full equation, effectively preconditioning the problem. This paper concentrates on the theoretical basis of the method, establishing local and global a priori error bounds.