A non-overlapping implicit predictor-corrector scheme for parabolic equations

Abstract

The explicit-implicit domain decomposition algorithm introduced by Dawson, Du and Dupont [6] is extended to more general convection-diffusion equations and arbitrary space dimensions with more general subdomains. The algorithm involves an explicit Euler predictor scheme on a coarse grid for interface values, an implicit Euler scheme on non-overlapping subdomains, and a fine grid correction at the interface. The purpose of this note is to develop convergence analysis based on the maximum principle.