On the convergence rate of the Dirichlet-Neumann iteration for coupled poisson problems on unstructured grids

We consider thermal fluid structure interaction with a partitioned approach, where typically, a finite volume and a finite element code would be coupled. As a model problem, we consider two coupled Poisson problems with heat conductivities l1, l2 in one dimension on intervals of length l1 and l2. Hereby, we consider linear discretizations on arbitrary meshes, such as finite volumes, finite differences, finite elements. For these, we prove that the convergence rate of the Dirichlet-Neumann iteration is given by l1l2/l2l1 and is thus independent of discretization and mesh.