%0 Journal Article
%T RTk mixed finite elements for some nonlinear problems.
%+ Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA)
%+ Institut de Mathématiques de Marseille (I2M)
%A Eymard, Robert
%A Gallouët, Thierry
%A Herbin, Raphaèle
%< avec comité de lecture
%@ 0378-4754
%J Mathematics and Computers in Simulation
%I Elsevier
%P 1-20
%8 2014-12
%D 2014
%R 10.1016/j.matcom.2014.11.013
%K gradient schemes
%K two phase flow
%K mixed finite element
%Z Mathematics [math]/Numerical Analysis [math.NA]Journal articles
%X We show that the discrete operators and spaces of gradient discretizations can be designed so that the corresponding gradient scheme for a linear diffusion problem be identical to the Raviart–Thomas RT k mixed finite element method for both the primal mixed finite element formulation and the hybrid dual formulation. We then give the hybrid dual RT 0 scheme for the approximation of a nonlinear model for two-phase flow in porous media; its convergence is then known thanks to a recent proof of the convergence of gradient schemes for this problem.
%G English
%2 https://hal.science/hal-01127963/document
%2 https://hal.science/hal-01127963/file/mamern-egh.pdf
%L hal-01127963
%U https://hal.science/hal-01127963
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ LAMA_UMR8050
%~ LAMA_EDP
%~ UPEC
%~ I2M
%~ I2M-2014-
%~ TDS-MACS
%~ UNIV-EIFFEL
%~ UPEM-UNIVEIFFEL