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.
DOI : 10.1051/m2an/2015005
Mots-clés : Heterogeneous diffusion problems, cell-centered methods, hybrid finite volumes, general meshes
@article{M2AN_2015__49_4_1063_0,
author = {Coatl\'even, Julien},
title = {Semi hybrid method for heterogeneous and anisotropic diffusion problems on general meshes},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1063--1084},
publisher = {EDP-Sciences},
volume = {49},
number = {4},
year = {2015},
doi = {10.1051/m2an/2015005},
mrnumber = {3371904},
zbl = {1327.65206},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2015005/}
}
TY - JOUR AU - Coatléven, Julien TI - Semi hybrid method for heterogeneous and anisotropic diffusion problems on general meshes JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2015 SP - 1063 EP - 1084 VL - 49 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2015005/ DO - 10.1051/m2an/2015005 LA - en ID - M2AN_2015__49_4_1063_0 ER -
%0 Journal Article %A Coatléven, Julien %T Semi hybrid method for heterogeneous and anisotropic diffusion problems on general meshes %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2015 %P 1063-1084 %V 49 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2015005/ %R 10.1051/m2an/2015005 %G en %F M2AN_2015__49_4_1063_0
Coatléven, Julien. Semi hybrid method for heterogeneous and anisotropic diffusion problems on general meshes. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 4, pp. 1063-1084. doi : 10.1051/m2an/2015005. http://www.numdam.org/articles/10.1051/m2an/2015005/
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