Parallel solution of Mixed Finite Element/Spectral Element systems for convection–diffusion equations on non-matching grids

A heterogeneous domain decomposition with non-matching grids is developed, extending the Aitken–Schwarz method [M. Garbey, D. Tromeur-Dervout, On some Aitken like acceleration of the Schwarz method, Internat. J. Numer. Methods Fluids 40 (2002) 1493–1513] which has proved to be efficient on metacomputing architectures. This novel numerical technique for the approximate solution of boundary value problems applies when the solution is assumed to possess many features in several subdomains such as in underground environmental problems with different geological layers. The numerical technique involves methods for the approximation and the solution of arising linear systems, as well as for parallel computing issues. We consider a natural coupling between the mixed finite element and spectral element approximations as well as the efficient solution of the coupled discrete systems on remote parallel computers with different architectures connected via a low speed network.