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

Authors:
Changfeng Li;Yirang Yuan
Affiliations:
School of Economics, Shandong University, Jinan 250100, China;Institute of Mathematics, Shandong University, Jinan 250100, China
Venue:
Applied Numerical Mathematics
Year:
2009

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Abstract

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 l^2 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.