Abstract: Combining the domain decomposition with upwind difference method,
the authors present the convection part of multidimensional parabolic problems is discretized by the 1-order upwind method and the modified 2-order upwind method. The proposed schemes rely on implicit procedures in subdomains and explicit calculation on the inter-domain boundaries. With certain stability conditions, convergence analysis is presented by the maximum principle and embedding theorem. Finally, numerical examples illustrating the value, accuracy and parallelism are shown.

Key words: Domain decomposition, Parallel computation, Upwind difference,
Error estimates