A Finite Volume Ventcell-Schwarz Algorithm for Advection-Diffusion Equations

This paper provides a new fully discrete domain decomposition algorithm for the advection diffusion reaction equation. It relies on the optimized Ventcell–Schwarz algorithm with a finite volume discretization of the subdomain problems. The scheme includes a wide range of advection fluxes with a special treatment on the boundary. A complete analysis of the scheme is presented, and the convergence of the algorithm to a discrete approximation of the equation using a modified convective flux is proved. Numerical illustrations of the efficiency of the discrete Ventcell– Schwarz algorithm are given.