A modified upwind difference domain decomposition method for convection–diffusion equations

A new, efficient and noniterative type of domain decomposition method is presented for three-dimensional convection–diffusion equations, whose convection term is handled by modified upwind differences. The whole domain is decomposed into several nonoverlapping subdomains. The values on inter-domain boundaries are calculated by reduced-dimensional solver and the solutions in subdomains are computed by implicit upwind procedures completely in parallel. With certain weakened stability constraint, error estimates in discrete l2 norm is discussed by introducing new inner products and techniques of prior estimates. Finally, the theoretical results are illustrated by linear and nonlinear numerical experiments.