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. 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

S. Bartels, M. Jensen, and R. Müller, Discontinuous Galerkin Finite Element Convergence for Incompressible Miscible Displacement Problems of Low Regularity, SIAM Journal on Numerical Analysis, vol.47, issue.5, pp.3720-3743, 2009.
DOI : 10.1137/070712079

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

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

C. Chainais-hillairet, S. Krell, and A. Mouton, Study of Discrete Duality Finite Volume Schemes for the Peaceman Model, SIAM Journal on Scientific Computing, vol.35, issue.6, pp.2928-2952, 2013.
DOI : 10.1137/130910555
URL : https://hal.archives-ouvertes.fr/hal-00790449

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, C. Pierre, and R. Turpault, A DDFV scheme for anisotropic and heterogeneous elliptic equations, application to a biomathematics problem: Electrocardiogram simulation, Proceedings of Finite Volumes for Complex Applications V, 2008.

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, The approximation of the pressure by a mixed method in the simulation of miscible displacement, RAIRO. Analyse num??rique, vol.17, issue.1, pp.17-33, 1983.
DOI : 10.1051/m2an/1983170100171

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.1069-1100, 2006.
DOI : 10.1051/m2an:2007001
URL : https://hal.archives-ouvertes.fr/hal-00009614

J. Droniou, Finite volume schemes for diffusion equations: Introduction to and review of modern methods, Mathematical Models and Methods in Applied Sciences, vol.24, issue.08, 2013.
DOI : 10.1142/S0218202514400041
URL : https://hal.archives-ouvertes.fr/hal-00813613

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

X. Feng, On Existence and Uniqueness Results for a Coupled System Modeling Miscible Displacement in Porous Media, Journal of Mathematical Analysis and Applications, vol.194, issue.3, pp.883-910, 1995.
DOI : 10.1006/jmaa.1995.1334

T. Gallouët and J. Latché, Compactness of discrete approximate solutions to parabolic PDEs - Application to a turbulence model, Communications on Pure and Applied Analysis, vol.11, issue.6, pp.2371-2391, 2012.
DOI : 10.3934/cpaa.2012.11.2371

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

T. F. Russell, Finite Elements With Characteristics for Two-Component Incompressible Miscible Displacement, SPE Reservoir Simulation Symposium, pp.123-135, 1982.
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