Explicit/implicit, conservative domain decomposition procedures for parabolic problems based on block-centered finite differences

Domain decomposition procedures for solving parabolic equations are considered. The underlying discretization consists of block-centered finite differences. In these procedures, fluxes at subdomain interfaces are calculated from the solution at the previous time level. These fluxes serve as Neumann boundary data for implicit, block-centered discretizations in the subdomains. A priori error estimates are presented, and numerical results examining the stability, accuracy, and parallelism of the scheme are presented.