The Lions domain decomposition algorithm on non-matching cell-centred finite volume meshes

A finite volume scheme for convection diffusion equations onnon-matching grids is presented. Sharp error estimates for H²solutions of the continuous problem are obtained. A finite volumeversion of an adaptation of the Schwarz algorithm due to P.L. Lions is then studied. For a fixed mesh, its convergencetowards the finite volume scheme on the whole domain is proven.Numerical experiments are performed to illustrate the theoreticalrate of convergence of the finite volume sequences of solutionsas the mesh is refined, together with the speed of convergenceof the Schwarz algorithm.