J. Adimurthi, G. D. Jaffré, . Veerappa, and . Gowda, Godunov-Type Methods for Conservation Laws with a Flux Function Discontinuous in Space, SIAM Journal on Numerical Analysis, vol.42, issue.1, pp.179-208, 2004.
DOI : 10.1137/S003614290139562X

S. Adimurthi, G. D. Mishra, . Veerapa, and . Gowda, OPTIMAL ENTROPY SOLUTIONS FOR CONSERVATION LAWS WITH DISCONTINUOUS FLUX-FUNCTIONS, Journal of Hyperbolic Differential Equations, vol.24, issue.04, pp.783-837, 2005.
DOI : 10.1137/S0036142900374974

B. Andreianov, P. Goatin, and N. Seguin, Finite volume schemes for locally constrained conservation laws, to appear in Num, Math, p.387806

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

T. Arbogast, The existence of weak solutions to single porosity and simple dual-porosity models of two-phase incompressible flow, Nonlinear Analysis: Theory, Methods & Applications, vol.19, issue.11, pp.1009-1031, 1992.
DOI : 10.1016/0362-546X(92)90121-T

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

M. Bertsch, R. Dal-passo, and C. J. Van-duijn, Analysis of Oil Trapping in Porous Media Flow, SIAM Journal on Mathematical Analysis, vol.35, issue.1, pp.245-267, 2003.
DOI : 10.1137/S0036141002407375

R. Bürger, K. H. Karlsen, and J. D. Towers, An Engquist???Osher-Type Scheme for Conservation Laws with Discontinuous Flux Adapted to Flux Connections, SIAM Journal on Numerical Analysis, vol.47, issue.3, pp.47-1684, 2009.
DOI : 10.1137/07069314X

F. Buzzi, M. Lenzinger, and B. Schweizer, Interface conditions for degenerate two-phase flow equations in one space dimension, Analysis, vol.1, issue.3, pp.29-299, 2009.
DOI : 10.1137/060675472

C. Cancès, Finite volume scheme for two-phase flows in heterogeneous porous media involving capillary pressure discontinuities, ESAIM: Mathematical Modelling and Numerical Analysis, vol.90, issue.5, pp.973-1001, 2009.
DOI : 10.1007/s002110100307

C. Cancès, Two-phase flows involving discontinuities on the capillary pressure, in " Finite Volumes for Complex Applications V : Problems and perspectives, Papers from the 5th Symposium held in Aussois, pp.249-256, 2008.

C. Cancès, Asymptotic behavior of two-phase flows in heterogeneous porous media for capillarity depending only of the space. I. Convergence to the optimal entropy solution, to appear in SIAM, J. Math. Anal

C. Cancès, Asymptotic behavior of two-phase flows in heterogeneous porous media for capillarity depending only of the space. II. Non-classical shocks to model oil-trapping, to appear in SIAM, J. Math. Anal

C. Cancès, T. Gallouët, and A. Porretta, Two-phase flows involving capillary barriers in heterogeneous porous media, Interfaces Free Bound, pp.239-258, 2009.

G. Chavent and J. Jaffré, Mathematical Models and Finite Elements for Reservoir Simulation, Studies in Mathematics and its Applications, 1986.

Z. Chen, Degenerate two-phase incompressible flow. I. Existence, uniqueness and regularity of a weak solution, J. Differential Equations, pp.171-203, 2001.
DOI : 10.1006/jdeq.2000.3848

URL : https://doi.org/10.1006/jdeq.2000.3848

R. M. Colombo and P. Goatin, A well posed conservation law with a variable unilateral constraint, Journal of Differential Equations, vol.234, issue.2, pp.654-675, 2007.
DOI : 10.1016/j.jde.2006.10.014

G. Enchéry, R. Eymard, and A. Michel, Numerical Approximation of a Two-phase Flow Problem in a Porous Medium with Discontinuous Capillary Forces, SIAM Journal on Numerical Analysis, vol.43, issue.6, pp.2402-2422, 2006.
DOI : 10.1137/040602936

A. Ern, I. Mozolevski, and L. Schuh, Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.23-24, pp.199-1491, 2010.
DOI : 10.1016/j.cma.2009.12.014

URL : https://hal.archives-ouvertes.fr/hal-00368026

B. G. Ersland, M. S. Espedal, and R. Nybø, Numerical methods for flow in a porous medium with internal boundaries, Computational Geosciences, vol.2, issue.3, pp.217-240, 1998.
DOI : 10.1023/A:1011554320427

G. Gagneux and M. Madaune-tort, Analyse mathématique de modèles non linéaires de l'ingénieriepétrolì ere, ) [Mathematics & Applications, 1996.

E. F. Kaasschieter, Solving the Buckley-Leverett equation with gravity in a heterogeneous porous medium, Computational Geosciences, vol.3, issue.1, pp.23-48, 1999.
DOI : 10.1023/A:1011574824970

J. Málek, J. Ne?as, M. Rokyta, and M. R. @bullet, Weak and measure-valued solutions to evolutionary PDEs, Applied Mathematics and Mathematical Computation, vol.13, 1996.
DOI : 10.1007/978-1-4899-6824-1

F. Otto, Initial-boundary value problem for a scalar conservation law, C. R. Acad. Sci. Paris Sér. I Math, vol.322, pp.729-734, 1996.

E. Yu and . Panov, Existence of strong traces for quasi-solutions of multidimensional conservation laws, J. Hyperbolic Differ. Equ, vol.4, pp.729-770, 2007.