The Lions domain decomposition algorithm on non matching cell-centered finite volume meshes
Résumé
A finite volume scheme for convection diffusion equation on non matching grids is presented. Sharp error estimates for $H^2$ solutions of the continuous problem are obtained. A finite volume version of an adaptation of the Schwarz algorithm due to P.L. Lions is then studied. For a fixed mesh, its convergence towards the finite volume scheme on the whole domain is proven. Numerical experiments are performed to illustrate the theoretical rate of convergence of the finite volume sequences of solutions as the mesh is refined, together with the speed of convergence of the Schwarz algorithm.