(untitled) (Journal of Computational Mathematics, 2002)
This paper provides a theoretical justification to a overlapping domain decomposition method applied to the solution of time-dependent convection-diffusion problems. The method is based on the partial upwind finite element scheme and the discrete strong maximum principle for steady problem. An error estimate in L^∞(0,T;L^∞(Ω)) is obtained and the fact that convergence factor ρ(τ,h)→ 0 exponentially as τ,h→ 0 is also proved under some usual conditions.