DDFV Ventcell Schwarz Algorithms

Over the last five years, classical and optimized Schwarz methods have been developed for (1) discretized with Discrete Duality Finite Volume (DDFV) schemes. Like for Discontinuous Galerkin methods, it is not a priori clear how to appropriately discretize transmission conditions. Two versions have been proposed for Robin transmission conditions in [? ] and [? ]. Only the second one leads to the expected rapid convergence rate of the optimized Schwarz algorithm, see [? ] for parabolic problems. The DDFV method needs a dual set of unknowns located on both vertices and “centers” of the initial mesh, which leads to two meshes, the primal and the dual one. This permits the reconstruction of two-dimensional discrete gradients located on a third partition of Ω, called the diamond mesh. A discrete divergence operator is also defined by duality. This method is particularly accurate in terms of gradient approximations, see the benchmark [? ] for problem (1) with η = 0, and also an extensive bibliography. A non-overlapping Schwarz method using Ventcell transmission conditions was first proposed in [? ]. For the model problem (1), the algorithm with two