https://hal.archives-ouvertes.fr/hal-03728206v1Coatléven, JulienJulienCoatlévenIFPEN - IFP Energies nouvelles - IFPEN - IFP Energies nouvellesUnconditionally stable small stencil enriched multiple point flux approximations of heterogeneous diffusion problems on general meshesHAL CCSD2022[MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA]Coatléven, Julien2022-07-20 10:43:352022-10-22 04:37:032022-07-22 12:04:44enPreprints, Working Papers, ...https://hal.archives-ouvertes.fr/hal-03728206v1application/pdf1We derive new multiple point flux approximations (MPFA) for the finite volume approximation of heterogeneous and anisotropic diffusion problems on general meshes, in dimension 2 and 3. The resulting methods are unconditionally stable while preserving the small stencil typical of MPFA finite volumes. The key idea is to solve local variational problems with a well designed stabilization term from which we deduce conservative flux instead of directly prescribing a flux formula and solving the usual flux continuity equations. The boundary conditions of our local variational problems are handled through additional cell-centered unknowns, leading to an overall scheme with the same number of unknowns than first-order discontinuous Galerkin methods. Convergence results follow from well established frameworks, while numerical experiments illustrate the good behavior of the method.