Semi hybrid method for heterogeneous and anisotropic diffusion problems on general meshes
IFP Énergies nouvelles, 1 et 4 avenue de Bois-Préau, 92852 Rueil-Malmaison,
Revised: 16 January 2015
Symmetric, unconditionnaly coercive schemes for the discretization of heterogeneous and anisotropic diffusion problems on general, possibly nonconforming 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.
Mathematics Subject Classification: 65N08 / 65N12 / 65N15
Key words: Heterogeneous diffusion problems / cell-centered methods / hybrid finite volumes / general meshes
© EDP Sciences, SMAI 2015