Semi hybrid method for heterogeneous and anisotropic diffusion problems on general meshes

Abstract

Symmetric, unconditionnaly coercive schemes for the discretization of heterogeneous and anisotropic diffusion problems on general, possibly conconforming meshes are developed and studied. These schemes are a further generalization of the Hybrid Mixed Method, which allows to use a general class of consistent gradients to construct them. While the schemes are in principle hybrid, many discrete gradients or the use of correct interpolation allow to eliminate the additional face unknowns. Convergence of the approximate solutions to minimal regularity solutions is proved for general tensors and meshes. Error estimates are derived under classical regularity assumptions. Numerical results illustrate the performance of the schemes.