I. Aavatsmark, T. Barkve, O. Bøe, and T. Mannseth, Discretization on Unstructured Grids for Inhomogeneous, Anisotropic Media. Part I: Derivation of the Methods, SIAM Journal on Scientific Computing, vol.19, issue.5, pp.1700-1716, 1998.
DOI : 10.1137/S1064827595293582

I. Aavatsmark, T. Barkve, O. Bøe, and T. Mannseth, Discretization on Unstructured Grids For Inhomogeneous, Anisotropic Media. Part II: Discussion And Numerical Results, SIAM Journal on Scientific Computing, vol.19, issue.5, pp.1717-1736, 1998.
DOI : 10.1137/S1064827595293594

B. Amaziane and M. Ossmani, Convergence analysis of an approximation to miscible fluid flows in porous media by combining mixed finite element and finite volume methods, Numerical Methods for Partial Differential Equations, vol.13, issue.3, pp.799-832, 2008.
DOI : 10.1002/num.20291

B. Andreianov, M. Bendahmane, and K. H. Karlsen, DISCRETE DUALITY FINITE VOLUME SCHEMES FOR DOUBLY NONLINEAR DEGENERATE HYPERBOLIC-PARABOLIC EQUATIONS, Journal of Hyperbolic Differential Equations, vol.07, issue.01, pp.1-67, 2010.
DOI : 10.1142/S0219891610002062
URL : https://hal.archives-ouvertes.fr/hal-00475752

B. Andreianov, F. Boyer, and F. Hubert, Discrete duality finite volume schemes for Leray???Lions???type elliptic problems on general 2D meshes, Numerical Methods for Partial Differential Equations, vol.152, issue.1, pp.145-195, 2007.
DOI : 10.1002/num.20170
URL : https://hal.archives-ouvertes.fr/hal-00005779

J. Bear, Dynamics of Fluids in Porous Media, Soil Science, vol.120, issue.2, 1972.
DOI : 10.1097/00010694-197508000-00022

M. Bessemoulin-chatard, C. Chainais-hillairet, and F. Filbet, On discrete functional inequalities for some finite volume schemes. submitted, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00672591

F. Boyer and F. Hubert, Finite Volume Method for 2D Linear and Nonlinear Elliptic Problems with Discontinuities, SIAM Journal on Numerical Analysis, vol.46, issue.6, pp.3032-3070, 2008.
DOI : 10.1137/060666196
URL : https://hal.archives-ouvertes.fr/hal-00110436

C. Chainais-hillairet and J. Droniou, Convergence Analysis of a Mixed Finite Volume Scheme for an Elliptic-Parabolic System Modeling Miscible Fluid Flows in Porous Media, SIAM Journal on Numerical Analysis, vol.45, issue.5, pp.2228-2258, 2007.
DOI : 10.1137/060657236
URL : https://hal.archives-ouvertes.fr/hal-00022910

Y. Coudì-ere and G. Manzini, The Discrete Duality Finite Volume Method for Convection-diffusion Problems, SIAM Journal on Numerical Analysis, vol.47, issue.6, pp.4163-4192, 2010.
DOI : 10.1137/080731219

Y. Coudì-ere, J. Vila, and P. Villedieu, Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem, ESAIM: Mathematical Modelling and Numerical Analysis, vol.33, issue.3, pp.493-516, 1999.
DOI : 10.1051/m2an:1999149

K. Domelevo and P. Omnes, A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids, ESAIM: Mathematical Modelling and Numerical Analysis, vol.39, issue.6, pp.1203-1249, 2005.
DOI : 10.1051/m2an:2005047

J. Douglas, Numerical methods for the flow of miscible fluids in porous media, 1984.

J. Douglas, J. , R. E. Ewing, and M. F. Wheeler, A time-discretization procedure for a mixed finite element approximation of miscible displacement in porous media, RAIRO. Analyse num??rique, vol.17, issue.3, pp.249-265, 1983.
DOI : 10.1051/m2an/1983170302491

J. Droniou, Finite volume schemes for fully non-linear elliptic equations in divergence form, ESAIM: Mathematical Modelling and Numerical Analysis, vol.40, issue.6, pp.1069-1088
DOI : 10.1051/m2an:2007001
URL : https://hal.archives-ouvertes.fr/hal-00009614

J. Droniou and R. Eymard, A mixed finite volume scheme for anisotropic diffusion problems on any grid, Numerische Mathematik, vol.59, issue.1, pp.35-71, 2006.
DOI : 10.1007/s00211-006-0034-1
URL : https://hal.archives-ouvertes.fr/hal-00005565

R. E. Ewing, T. F. Russell, and M. F. Wheeler, Simulation of Miscible Displacement Using Mixed Methods and a Modified Method of Characteristics, SPE Reservoir Simulation Symposium, pp.71-81, 1983.
DOI : 10.2118/12241-MS

R. E. Ewing, T. F. Russell, and M. F. Wheeler, Convergence analysis of an approximation of miscible displacement in porous media by mixed finite elements and a modified method of characteristics, Computer Methods in Applied Mechanics and Engineering, vol.47, issue.1-2, pp.73-92, 1984.
DOI : 10.1016/0045-7825(84)90048-3

R. Eymard, T. Gallouët, and R. Herbin, Finite volume methods, Handbook of numerical analysis, pp.715-1022, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00346077

R. Eymard, T. Gallouët, and R. Herbin, A new finite volume scheme for anisotropic diffusion problems on general grids: convergence analysis, Comptes Rendus Mathematique, vol.344, issue.6, pp.403-406, 2007.
DOI : 10.1016/j.crma.2007.01.024

R. Eymard, T. Gallouët, and R. Herbin, Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces, IMA Journal of Numerical Analysis, vol.30, issue.4, pp.1009-1043, 2010.
DOI : 10.1093/imanum/drn084

R. Eymard, G. Henry, R. Herbin, F. Hubert, R. Klöfkorn et al., 3D Benchmark on Discretization Schemes for Anisotropic Diffusion Problems on General Grids, Proceedings of Finite Volumes for Complex Applications VI, pp.95-130, 2011.
DOI : 10.1007/978-3-642-20671-9_89
URL : https://hal.archives-ouvertes.fr/hal-00580549

R. Herbin and F. Hubert, Benchmark on discretization schemes for anisotropic diffsion problems on general grids, Proceedings of Finite Volumes for Complex Applications V, 2008.

F. Hermeline, A Finite Volume Method for the Approximation of Diffusion Operators on Distorted Meshes, Journal of Computational Physics, vol.160, issue.2, pp.481-499, 2000.
DOI : 10.1006/jcph.2000.6466

F. Hermeline, Approximation of diffusion operators with discontinuous tensor coefficients on distorted meshes, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.16-18, pp.16-181939, 2003.
DOI : 10.1016/S0045-7825(02)00644-8

J. Jaffré and J. E. Roberts, Upstream weighting and mixed finite elements in the simulation of miscible displacements, ESAIM: Mathematical Modelling and Numerical Analysis, vol.19, issue.3, pp.443-460, 1985.
DOI : 10.1051/m2an/1985190304431

A. Le and P. Omnes, Discrete poincaré inequalities for arbitrary meshes in the discrete duality finite volume context. submitted, 2012.

T. F. Russell, Finite Elements With Characteristics for Two-Component Incompressible Miscible Displacement, SPE Reservoir Simulation Symposium
DOI : 10.2118/10500-MS

H. Wang, D. Liang, R. E. Ewing, S. L. Lyons, and G. Qin, An Approximation to Miscible Fluid Flows in Porous Media with Point Sources and Sinks by an Eulerian--Lagrangian Localized Adjoint Method and Mixed Finite Element Methods, SIAM Journal on Scientific Computing, vol.22, issue.2, pp.561-581, 2000.
DOI : 10.1137/S1064827598349215

H. Wang, D. Liang, R. E. Ewing, S. L. Lyons, and G. Qin, An improved numerical simulator for different types of flows in porous media, Numerical Methods for Partial Differential Equations, vol.15, issue.3, pp.343-362, 2003.
DOI : 10.1002/num.10045