Starting from the recently introduced virtual element method, we construct new diffusion fluxes in two and three dimensions that give birth to symmetric, unconditionally coercive finite volume like schemes for the discretization of heterogeneous and anisotropic diffusion-reaction problems on general, possibly nonconforming meshes. Convergence of the approximate solutions is proved for general tensors and meshes. Error estimates are derived under classical regularity assumptions. Numerical results illustrate the performance of the scheme. The link with the original vertex approximate gradient scheme is emphasized.
Accepté le :
DOI : 10.1051/m2an/2016036
Mots clés : Heterogeneous diffusion-reaction problems, finite volumes, general meshes, virtual element method
@article{M2AN_2017__51_3_797_0, author = {Coatl\'even, Julien}, title = {A virtual volume method for heterogeneous and anisotropic diffusion-reaction problems on general meshes}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {797--824}, publisher = {EDP-Sciences}, volume = {51}, number = {3}, year = {2017}, doi = {10.1051/m2an/2016036}, mrnumber = {3666647}, zbl = {1371.65113}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2016036/} }
TY - JOUR AU - Coatléven, Julien TI - A virtual volume method for heterogeneous and anisotropic diffusion-reaction problems on general meshes JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 797 EP - 824 VL - 51 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2016036/ DO - 10.1051/m2an/2016036 LA - en ID - M2AN_2017__51_3_797_0 ER -
%0 Journal Article %A Coatléven, Julien %T A virtual volume method for heterogeneous and anisotropic diffusion-reaction problems on general meshes %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 797-824 %V 51 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2016036/ %R 10.1051/m2an/2016036 %G en %F M2AN_2017__51_3_797_0
Coatléven, Julien. A virtual volume method for heterogeneous and anisotropic diffusion-reaction problems on general meshes. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 3, pp. 797-824. doi : 10.1051/m2an/2016036. http://www.numdam.org/articles/10.1051/m2an/2016036/
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