R. A. Adams, Sobolev Spaces, 1975.

M. Ahmed, E. , J. Jaffré, and J. E. Roberts, A reduced fracture model for two-phase flow with different rock types, Mathematics and Computers in Simulation, vol.137, 2016.
DOI : 10.1016/j.matcom.2016.10.005

URL : https://hal.archives-ouvertes.fr/hal-01119986

R. Ahmed, M. Edwards, S. Lamine, B. Huisman, and M. Pal, Control-volume distributed multi-point flux approximation coupled with a lower-dimensional fracture model, Journal of Computational Physics, vol.284, pp.462-489, 2015.
DOI : 10.1016/j.jcp.2014.12.047

R. Ahmed, M. G. Edwards, S. Lamine, B. A. Huisman, and M. Pal, Three-dimensional control-volume distributed multi-point flux approximation coupled with a lower-dimensional surface fracture model, Journal of Computational Physics, vol.303, pp.470-497, 2015.
DOI : 10.1016/j.jcp.2015.10.001

C. Alboin, J. Jaffré, J. Roberts, and C. Serres, Modeling fractures as interfaces for flow and transport in porous media, pp.13-24, 2002.
DOI : 10.1090/conm/295/04999

P. Angot, F. Boyer, and F. Hubert, Asymptotic and numerical modelling of flows in fractured porous media, ESAIM: Mathematical Modelling and Numerical Analysis, vol.29, issue.2, pp.239-275, 2009.
DOI : 10.1016/j.advwatres.2005.09.001

URL : https://hal.archives-ouvertes.fr/hal-00127023

P. F. Antonietti, L. Formaggia, A. Scotti, M. Verani, and N. Verzotti, Mimetic finite difference approximation of flows in fractured porous media, ESAIM: Mathematical Modelling and Numerical Analysis, vol.50, issue.3, pp.809-832, 2016.
DOI : 10.1016/S1570-8659(05)80041-9

S. N. Antontsev, A. V. Kazhikhov, and V. N. Monakhov, Boundary value problems in mechanics of nonhomogeneous fluids, Studies in Mathematics and its Applications, p.22, 1990.

G. Barenblatt, I. Zheltov, and I. Kochina, Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata], Journal of Applied Mathematics and Mechanics, vol.24, issue.5, pp.825-864, 1960.
DOI : 10.1016/0021-8928(60)90107-6

S. Berrone, S. Pieraccini, and S. Scialò, An optimization approach for large scale simulations of discrete fracture network flows, Journal of Computational Physics, vol.256, pp.838-853, 2014.
DOI : 10.1016/j.jcp.2013.09.028

I. I. Bogdanov, V. V. Mourzenko, J. Thovert, and P. M. Adler, Two-phase flow through fractured porous media, Physical Review E, vol.26, issue.2, 2003.
DOI : 10.1029/WR026i007p01483

URL : https://hal.archives-ouvertes.fr/hal-00417570

J. Bonelle and A. A. Ern, Analysis of Compatible Discrete Operator schemes for elliptic problems on polyhedral meshes, ESAIM: Mathematical Modelling and Numerical Analysis, vol.48, issue.2, pp.553-581, 2014.
DOI : 10.1515/9781400877577

URL : https://hal.archives-ouvertes.fr/hal-00751284

K. Brenner, Méthodes de volumes finis sur maillages quelconques pour des systèmes d'évolution non linéaires, 2011.

K. Brenner, C. Cancès, and D. Hilhorst, Finite volume approximation for an immiscible two-phase flow in porous media with discontinuous capillary pressure, Computational Geosciences, vol.21, issue.4, 2013.
DOI : 10.1007/BF00615335

URL : https://hal.archives-ouvertes.fr/hal-00675681

K. Brenner, M. Groza, C. Guichard, G. Lebeau, and R. Masson, Gradient discretization of hybrid dimensional Darcy flows in fractured porous media, Numerische Mathematik, vol.16, issue.7, pp.569-609, 2016.
DOI : 10.1007/s10596-011-9267-x

URL : https://hal.archives-ouvertes.fr/hal-01097704

K. Brenner, M. Groza, C. Guichard, and R. Masson, Vertex Approximate Gradient scheme for hybrid-dimensional two-phase Darcy flows in fractured porous media, ESAIM: Mathematical Modelling and Numerical Analysis, vol.2, issue.49, pp.303-330, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01313353

K. Brenner, M. Groza, L. Jeannin, R. Masson, and J. Pellerin, Immiscible twophase darcy flow model accouting for vanishing and discontinuous capillary pressures: application to the flow in fracture porous media, ECMOR XV-15th European Conference on the Mathematics of Oil Recovery, 2016.

K. Brenner and R. Masson, Convergence of a Vertex centered Discretization of Two-Phase Darcy flows on General Meshes, Int. Journal of Finite, vol.Methods, issue.10, pp.15-2013

F. Brezzi, K. Lipnikov, and V. Simoncini, A FAMILY OF MIMETIC FINITE DIFFERENCE METHODS ON POLYGONAL AND POLYHEDRAL MESHES, Mathematical Models and Methods in Applied Sciences, vol.19, issue.10, pp.1533-1552, 2005.
DOI : 10.1016/0096-3003(83)90023-1

C. Cancès, Finite volume scheme for two-phase flows in heterogeneous porous media involving capillary pressure discontinuities. M2AN, Mathematical Modelling and Numerical Analysis, pp.973-1001, 2009.

C. Cancès and M. Pierre, An Existence Result for Multidimensional Immiscible Two-Phase Flows with Discontinuous Capillary Pressure Field, SIAM Journal on Mathematical Analysis, vol.44, issue.2, pp.966-992, 2012.
DOI : 10.1137/11082943X

G. Chavent and J. Jaffré, Mathematical models and finite elements for reservoir simulation, Studies in Mathematics and its Applications, 1986.

C. D. Angelo and A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids, ESAIM: Mathematical Modelling and Numerical Analysis, vol.46, issue.2, pp.465-489, 2012.

J. Demmel, S. Eisenstat, J. Gilbert, X. Li, and J. Liu, A Supernodal Approach to Sparse Partial Pivoting, SIAM Journal on Matrix Analysis and Applications, vol.20, issue.3, pp.720-750, 1999.
DOI : 10.1137/S0895479895291765

]. J. Droniou, Intégration et espaces de sobolev à valeurs vecto- rielles, 2001.

J. Droniou and R. Eymard, Uniform-in-time convergence of numerical methods for non-linear degenerate parabolic equations, Numerische Mathematik, vol.33, issue.1, pp.721-766, 2016.
DOI : 10.1137/0733004

J. Droniou, R. Eymard, and P. Feron, Gradient Schemes for Stokes problem, IMA Journal of Numerical Analysis, vol.36, issue.4, pp.1636-1669, 2016.
DOI : 10.1093/imanum/drv061

URL : https://hal.archives-ouvertes.fr/hal-01070703

J. Droniou, R. Eymard, T. Gallouët, C. Guichard, and R. Herbin, The gradient discretisation method: A framework for the discretisation of linear and nonlinear elliptic and parabolic problems, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01382358

J. Droniou, R. Eymard, T. Gallouët, and R. Herbin, A UNIFIED APPROACH TO MIMETIC FINITE DIFFERENCE, HYBRID FINITE VOLUME AND MIXED FINITE VOLUME METHODS, Mathematical Models and Methods in Applied Sciences, vol.17, issue.02, pp.265-295, 2010.
DOI : 10.1007/s10596-004-3771-1

URL : https://hal.archives-ouvertes.fr/hal-00346077

J. Droniou, R. Eymard, T. Gallouët, and R. Herbin, GRADIENT SCHEMES: A GENERIC FRAMEWORK FOR THE DISCRETISATION OF LINEAR, NONLINEAR AND NONLOCAL ELLIPTIC AND PARABOLIC EQUATIONS, Mathematical Models and Methods in Applied Sciences, vol.93, issue.13, pp.2395-2432, 2013.
DOI : 10.1023/A:1008009714131

URL : https://hal.archives-ouvertes.fr/hal-00751551

J. Droniou, R. Eymard, and R. Herbin, Gradient schemes: Generic tools for the numerical analysis of diffusion equations, ESAIM: Mathematical Modelling and Numerical Analysis, vol.50, issue.3, pp.749-781, 2016.
DOI : 10.1051/m2an/2015079

URL : https://hal.archives-ouvertes.fr/hal-01150517

J. Droniou, R. Eymard, and K. S. Talbot, Convergence in C ([0, T ]; L 2 (??)) of weak solutions to perturbed doubly degenerate parabolic equations, Journal of Differential Equations, vol.260, issue.11, pp.7821-7860, 2016.
DOI : 10.1016/j.jde.2016.02.004

URL : https://hal.archives-ouvertes.fr/hal-01278409

J. Droniou, J. Hennicker, and R. Masson, Uniform-in-time convergence of numerical schemes for a model of diphasic flow in a discrete fractured network media, 2016.

J. Droniou and K. S. Talbot, On a Miscible Displacement Model in Porous Media Flow with Measure Data, SIAM Journal on Mathematical Analysis, vol.46, issue.5, pp.3158-3175, 2014.
DOI : 10.1137/130949294

C. J. Duijn, J. Molenaar, and M. J. Neef, The effect of capillary forces on immiscible two-phase flow in heterogeneous porous media, Transport in Porous Media, vol.10, issue.7, pp.71-93, 1995.
DOI : 10.1016/B978-0-12-434065-7.50021-6

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, C. Guichard, and R. Herbin, Small-stencil 3D schemes for diffusive flows in porous media, ESAIM: Mathematical Modelling and Numerical Analysis, vol.228, issue.2, pp.265-290, 2012.
DOI : 10.1016/j.jcp.2009.05.002

URL : https://hal.archives-ouvertes.fr/hal-00542667

R. Eymard, C. Guichard, R. Herbin, and R. Masson, Vertex-centred discretization of multiphase compositional Darcy flows on general meshes, Computational Geosciences, vol.53, issue.4, pp.987-1005, 2012.
DOI : 10.2118/5734-PA

URL : https://hal.archives-ouvertes.fr/hal-01238550

R. Eymard, C. Guichard, R. Herbin, and R. Masson, Gradient schemes for two-phase flow in heterogeneous porous media and Richards equation, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f??r Angewandte Mathematik und Mechanik, vol.7, issue.1, pp.560-585, 2014.
DOI : 10.1002/pamm.200700165

URL : https://hal.archives-ouvertes.fr/hal-00740367

R. Eymard, C. Guichard, R. Herbin, and R. Masson, TP or not TP, that is the question, Computational Geosciences, vol.41, issue.4, pp.285-296, 2014.
DOI : 10.1137/S0036142900382739

URL : https://hal.archives-ouvertes.fr/hal-00801648

R. Eymard, R. Herbin, and A. Michel, Mathematical study of a petroleum-engineering scheme, ESAIM: Mathematical Modelling and Numerical Analysis, vol.15, issue.6, pp.937-972, 2003.
DOI : 10.1093/imanum/15.3.405

I. Faille, A. Fumagalli, J. Jaffré, and J. Robert, Reduced models for flow in porous media containing faults with discretization using hybrid finite volume schemes, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01162048

I. Faille, A. Fumagalli, J. Jaffré, and J. E. Roberts, Model reduction and discretization using hybrid finite volumes for flow in porous media containing faults, Computational Geosciences, vol.16, issue.7, pp.317-339, 2016.
DOI : 10.1007/s10596-011-9267-x

URL : https://hal.archives-ouvertes.fr/hal-01395454

E. Flauraud, F. Nataf, I. Faille, and R. Masson, Domain decomposition for an asymptotic geological fault modeling, Comptes Rendus M??canique, vol.331, issue.12, pp.849-855, 2003.
DOI : 10.1016/j.crme.2003.09.009

L. Formaggia, A. Fumagalli, A. Scotti, and P. Ruffo, A reduced model for Darcy???s problem in networks of fractures, ESAIM: Mathematical Modelling and Numerical Analysis, vol.48, issue.4, pp.1089-1116, 2014.
DOI : 10.1002/9783527636693

A. Fumagalli, A. Scotti, A. Cangiani, R. L. Davidchack, E. Georgoulis et al., A reduced model for flow and transport in fractured porous media with nonmatching grids, Numerical Mathematics and Advanced Applications, pp.499-507, 2013.

M. Groza, Modélisation et discrétisation des écoulements diphasiques en milieux poreux avec réseaux de fractures discrètes, 2016.

H. Haegland, A. Assteerawatt, H. Dahle, G. Eigestad, and R. Helmig, Comparison of cell- and vertex-centered discretization methods for flow in a two-dimensional discrete-fracture???matrix system, Advances in Water Resources, vol.32, issue.12, pp.1740-1755, 2009.
DOI : 10.1016/j.advwatres.2009.09.006

H. Hoteit and A. Firoozabadi, An efficient numerical model for incompressible two-phase flow in fractured media, Advances in Water Resources, vol.31, issue.6, pp.891-905, 2008.
DOI : 10.1016/j.advwatres.2008.02.004

J. Jaffré, M. Mnejja, and J. Roberts, A discrete fracture model for two-phase flow with matrix-fracture interaction, Procedia Computer Science, vol.4, pp.967-973, 2011.
DOI : 10.1016/j.procs.2011.04.102

J. Jaffré, M. Mnejja, and J. E. Roberts, A discrete fracture model for two-phase flow with matrix-fracture interaction, Procedia Computer Science, vol.4, pp.967-973, 2011.
DOI : 10.1016/j.procs.2011.04.102

D. Jansen, Identifikation des mehrkontinuum?modells zur simulation des stofftransportes in multiporösen festgesteinsaquiferen, Lehrstuhl und Institut für Wasserbau und Wasserwirtschaft, RWTH Aachen, 1999.

M. Karimi-fard, L. Durlofsky, and K. Aziz, An Efficient Discrete-Fracture Model Applicable for General-Purpose Reservoir Simulators, SPE Journal, vol.9, issue.02, pp.227-236, 2004.
DOI : 10.2118/88812-PA

H. Kazemi, Pressure Transient Analysis of Naturally Fractured Reservoirs with Uniform Fracture Distribution, Society of Petroleum Engineers Journal, vol.9, issue.04, pp.451-462, 1969.
DOI : 10.2118/2156-A

V. Martin, J. Jaffré, and J. E. Roberts, Modeling Fractures and Barriers as Interfaces for Flow in Porous Media, SIAM Journal on Scientific Computing, vol.26, issue.5, pp.1667-1691, 2005.
DOI : 10.1137/S1064827503429363

URL : https://hal.archives-ouvertes.fr/inria-00071735

S. K. Matthai, A. A. Mezentsev, and M. Belayneh, Finite Element - Node-Centered Finite-Volume Two-Phase-Flow Experiments With Fractured Rock Represented by Unstructured Hybrid-Element Meshes, SPE Reservoir Evaluation & Engineering, vol.10, issue.06, pp.740-756, 2007.
DOI : 10.2118/93341-PA

A. Michel, A Finite Volume Scheme for Two-Phase Immiscible Flow in Porous Media, SIAM Journal on Numerical Analysis, vol.41, issue.4, pp.1301-1317, 2003.
DOI : 10.1137/S0036142900382739

J. E. Monteagudo and A. Firoozabadi, Control-Volume Model for Simulation of Water Injection in Fractured Media: Incorporating Matrix Heterogeneity and Reservoir Wettability Effects, SPE Journal, vol.12, issue.03, pp.355-366, 2007.
DOI : 10.2118/98108-PA

K. Pruess and T. Narasimhan, A Practical Method for Modeling Fluid and Heat Flow in Fractured Porous Media, Society of Petroleum Engineers Journal, vol.25, issue.01, pp.14-26, 1985.
DOI : 10.2118/10509-PA

P. Raviart, Résolution Des Modèles Aux Dérivées Partielles, Ecole Polytechnique, 1992.

V. Reichenberger, H. Jakobs, P. Bastian, and R. Helmig, A mixed-dimensional finite volume method for two-phase flow in fractured porous media, Advances in Water Resources, vol.29, issue.7, pp.1020-1036, 2006.
DOI : 10.1016/j.advwatres.2005.09.001

Y. Saad, Iterative Methods for Sparse Linear Systems, 2003.
DOI : 10.1137/1.9780898718003

M. Sahimi, Flow and transport in porous media and fractured rock: from classical methods to modern approaches, 2011.
DOI : 10.1002/9783527636693

T. Sandve, I. Berre, and J. Nordbotten, An efficient multi-point flux approximation method for Discrete Fracture???Matrix simulations, Journal of Computational Physics, vol.231, issue.9, pp.3784-3800, 2012.
DOI : 10.1016/j.jcp.2012.01.023

N. Schwenck, B. Flemisch, R. Helmig, and B. Wohlmuth, Dimensionally reduced flow models in fractured porous media: crossings and boundaries, Computational Geosciences, vol.23, issue.3, pp.1219-1230, 2015.
DOI : 10.1029/WR023i003p00467

B. Singhal and R. Gupta, Applied Hydrogeology of Fractured Rocks, 2010.

X. Tunc, I. Faille, T. Gallouët, M. C. Cacas, and P. Havé, A model for conductive faults with non-matching grids, Computational Geosciences, vol.81, issue.6, pp.277-296, 2012.
DOI : 10.2118/17992-PA

J. Warren and P. Root, The Behavior of Naturally Fractured Reservoirs, Society of Petroleum Engineers Journal, vol.3, issue.03, pp.245-55, 1963.
DOI : 10.2118/426-PA

F. Xing, R. Masson, and S. Lopez, Parallel Vertex Approximate Gradient discretization of hybrid-dimensional Darcy flow and transport in discrete fracture networks, Computational Geosciences, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01272498