An Iterative domain decomposition algorithm for a nonlinear convection-diffusion problem

Abstract

This article describes an iterative domain decomposition algorithm for solving nonlinear singularly perturbed convection-diusi on problems where convection is dominant. The domain decomposition algorithm consists of the two iterative processes: outer iterations and inner iterations. One outer iterative step represents computing nonlinear dierence subproblems on overlapping subdomains in serial according to upwind error propagation (the multiplicative Schwarz method). At the level of the inner iterations, each nonlinear subproblem is solved by the monotone additive Schwarz algorithm. The advantages of the algorithm are that the algorithm solves only linear discrete systems at each iterative step, converges monotonically to the exact solution of the system, and is potentially parallelisable. Results of numerical experiments are presented.