A. Ambroso, C. Chalons, F. Coquel, T. Galié, E. Godlewski et al., The drift-flux asymptotic limit of barotropic two-phase two-pressure models, Communications in Mathematical Sciences, vol.6, issue.2, pp.521-529, 2008.
DOI : 10.4310/CMS.2008.v6.n2.a13

A. Ambroso, C. Chalons, F. Coquel, E. Godlewski, F. Lagoutì-ere et al., Coupling of general Lagrangian systems, Mathematics of Computation, vol.77, issue.262, pp.909-941, 2008.
DOI : 10.1090/S0025-5718-07-02064-9

A. Ambroso, C. Chalons, F. Coquel, E. Godlewski, F. Lagoutì-ere et al., Extension of interface coupling to general Lagrangian systems, In " Numerical mathematics and advanced applications, pp.852-860, 2006.

A. Ambroso, C. Chalons, F. Coquel, E. Godlewski, F. Lagoutì-ere et al., The coupling of homogeneous models for two-phase flows, Int. J. Finite, vol.4, p.39, 2007.
URL : https://hal.archives-ouvertes.fr/hal-01117451

A. Ambroso, C. Chalons, F. Coquel, E. Godlewski, F. Lagoutì-ere et al., Relaxation methods and coupling procedures, International Journal for Numerical Methods in Fluids, vol.71, issue.8, pp.1123-1129, 2008.
DOI : 10.1002/fld.1680

P. Amorim, P. G. Lefloch, and B. Okutmustur, Finite volume schemes on Lorentzian manifolds, Communications in Mathematical Sciences, vol.6, issue.4, pp.1059-1086, 2008.
DOI : 10.4310/CMS.2008.v6.n4.a13

F. Bachmann and J. Vovelle, Existence and Uniqueness of Entropy Solution of Scalar Conservation Laws with a Flux Function Involving Discontinuous Coefficients, Communications in Partial Differential Equations, vol.39, issue.3, pp.371-395, 2006.
DOI : 10.1142/S0218202503002477

URL : https://hal.archives-ouvertes.fr/hal-00447307

F. Bouchut, Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources, 2004.

B. Boutin, C. Chalons, and R. , EXISTENCE RESULT FOR THE COUPLING PROBLEM OF TWO SCALAR CONSERVATION LAWS WITH RIEMANN INITIAL DATA, Mathematical Models and Methods in Applied Sciences, vol.20, issue.10, pp.1859-1898, 2010.
DOI : 10.1142/S0218202510004817

URL : https://hal.archives-ouvertes.fr/hal-00871839

B. Boutin, F. Coquel, and E. Godlewski, Dafermos's regularization for interface coupling of conservation laws, Hyp2006 Conference Proceedings, 2008.

B. Boutin, F. Coquel, and L. P. , Coupling techniques for nonlinear hyperbolic equations. I Self-similar diffusion for thin interfaces, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.141, issue.05, pp.141-921, 2011.
DOI : 10.1017/S0308210510001459

URL : https://hal.archives-ouvertes.fr/hal-00564176

B. Boutin, F. Coquel, and L. P. , Coupling techniques for nonlinear hyperbolic equations. II, in preparation
URL : https://hal.archives-ouvertes.fr/hal-00564176

B. Boutin, F. Coquel, and L. P. , Coupling techniques for nonlinear hyperbolic equations. III. A regularization method based on thick interfaces, SIAM J. Numer. Anal, pp.51-1108, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00564176

R. Bürger and K. H. Karlsen, Conservation laws with discontinuous flux: a short introduction, Journal of Engineering Mathematics, vol.175, issue.3-4, pp.241-247, 2008.
DOI : 10.1007/s10665-008-9213-7

C. Chalons, P. Raviart, and N. Seguin, The interface coupling of the gas dynamics equations, Quarterly of Applied Mathematics, vol.66, issue.4, pp.659-705, 2008.
DOI : 10.1090/S0033-569X-08-01087-X

B. Cockburn, F. Coquel, and L. P. , Convergence of the Finite Volume Method for Multidimensional Conservation Laws, SIAM Journal on Numerical Analysis, vol.32, issue.3, pp.687-705, 1995.
DOI : 10.1137/0732032

B. Cockburn, F. Coquel, and L. P. , An error estimate for finite volume methods for multidimensional conservation laws, Mathematics of Computation, vol.63, issue.207, pp.77-103, 1994.
DOI : 10.1090/S0025-5718-1994-1240657-4

F. Coquel and P. G. Lefloch, Convergence of Finite Difference Schemes for Conservation Laws in Several Space Dimensions: A General Theory, SIAM Journal on Numerical Analysis, vol.30, issue.3, pp.310-455, 1990.
DOI : 10.1137/0730033

F. Coquel and P. G. Lefloch, Convergence of Finite Difference Schemes for Conservation Laws in Several Space Dimensions: A General Theory, SIAM Journal on Numerical Analysis, vol.30, issue.3, pp.675-700, 1993.
DOI : 10.1137/0730033

F. Coquel and P. G. Lefloch, Convergence of finite difference schemes for conservation laws in several space dimensions: the corrected antidiffusive flux approach, Mathematics of Computation, vol.57, issue.195, pp.169-210, 1991.
DOI : 10.1090/S0025-5718-1991-1079010-2

M. G. Crandall and A. Majda, Monotone difference approximations for scalar conservation laws, Mathematics of Computation, vol.34, issue.149, pp.1-21, 1980.
DOI : 10.1090/S0025-5718-1980-0551288-3

R. J. Diperna, Measure-valued solutions to conservation laws, Archive for Rational Mechanics and Analysis, vol.2, issue.3, pp.223-270, 1985.
DOI : 10.1007/BF00752112

D. Maso, G. Lefloch, P. G. Murat, and F. , Definition and weak stability of nonconservative products, J. Math. Pures Appl, vol.74, pp.483-548, 1995.

F. Dubois and P. G. Lefloch, Boundary conditions for nonlinear hyperbolic systems of conservation laws, Journal of Differential Equations, vol.71, issue.1, pp.93-122, 1988.
DOI : 10.1016/0022-0396(88)90040-X

R. Eymard, T. Gallouët, and R. Herbin, The finite volume method, Handbook Numer. Anal., VII, North-Holland, pp.713-1020, 2000.

P. Goatin and P. G. Lefloch, The Riemann problem for a class of resonant hyperbolic systems of balance laws, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.21, issue.6, pp.881-902, 2004.
DOI : 10.1016/j.anihpc.2004.02.002

E. Godlewski, L. Thanh, K. , and R. , The numerical interface coupling of nonlinear hyperbolic systems of conservation laws: II. The case of systems, ESAIM: Mathematical Modelling and Numerical Analysis, vol.39, issue.4, pp.39-649, 2005.
DOI : 10.1051/m2an:2005029

URL : https://hal.archives-ouvertes.fr/hal-00113734

E. Godlewski and P. Raviart, The numerical interface coupling of nonlinear hyperbolic systems of conservation laws: I. The scalar case, Numerische Mathematik, vol.97, issue.1, pp.81-130, 2004.
DOI : 10.1007/s00211-002-0438-5

A. Guelfi, D. Bestion, M. Boucker, P. Boudier, P. Fillion et al., NEPTUNE: A New Software Platform for Advanced Nuclear Thermal Hydraulics, Nuclear Science and Engineering, vol.156, issue.3, pp.281-324, 2007.
DOI : 10.13182/NSE05-98

P. Helluy and N. Seguin, Relaxation models of phase transition flows, ESAIM: Mathematical Modelling and Numerical Analysis, vol.40, issue.2, pp.331-352, 2006.
DOI : 10.1051/m2an:2006015

URL : https://hal.archives-ouvertes.fr/hal-00139607

K. T. Joseph and P. G. Lefloch, Boundary layers in weak solutions to hyperbolic conservation laws, Arch. Rational Mech Anal, pp.47-88, 1999.

D. Kröner, Finite volume schemes in multidimensions, in " Numerical analysis, Pitman Res. Notes Math. Ser, vol.380, pp.179-192, 1997.

S. Kruzkov, FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES, Mathematics of the USSR-Sbornik, vol.10, issue.2, pp.217-243, 1970.
DOI : 10.1070/SM1970v010n02ABEH002156

P. G. Lefloch, Propagating phase boundaries: Formulation of the problem and existence via the Glimm method, Archive for Rational Mechanics and Analysis, vol.2, issue.2, pp.153-197, 1993.
DOI : 10.1007/BF00695275

P. G. Lefloch, Hyperbolic Systems of Conservation Laws: The Theory of Classical and Nonclassical Shock Waves, Applied Mechanics Reviews, vol.56, issue.4, 2002.
DOI : 10.1115/1.1579455

P. G. Lefloch, Kinetic relations for undercompressive shock waves. Physical, mathematical, and numerical issues, Contemporary Mathematics, vol.526, pp.237-272, 2010.
DOI : 10.1090/conm/526/10384

P. G. Lefloch and T. Liu, Existence theory for nonlinear hyperbolic systems in nonconservative form, Forum Math, vol.5, pp.261-280, 1993.

P. G. Lefloch, W. Neves, and B. Okutmustur, Hyperbolic conservation laws on manifolds. An error estimate for finite volume schemes, Acta Mathematica Sinica, English Series, vol.350, issue.7, pp.1041-1066, 2009.
DOI : 10.1007/s10114-009-8090-y

URL : https://hal.archives-ouvertes.fr/hal-00121701

P. G. Lefloch and B. Okutmustur, Hyperbolic conservation laws on spacetimes. A finite volume scheme based on differential forms, Far East J. Math. Sci, pp.31-49, 2008.
DOI : 10.1007/978-1-4419-9554-4_21

URL : http://arxiv.org/abs/1006.2439

S. J. Osher, Riemann Solvers, the Entropy Condition, and Difference, SIAM Journal on Numerical Analysis, vol.21, issue.2, pp.217-235, 1984.
DOI : 10.1137/0721016

N. Seguin and J. Vovelle, ANALYSIS AND APPROXIMATION OF A SCALAR CONSERVATION LAW WITH A FLUX FUNCTION WITH DISCONTINUOUS COEFFICIENTS, Mathematical Models and Methods in Applied Sciences, vol.13, issue.02, pp.221-257, 2003.
DOI : 10.1142/S0218202503002477

URL : https://hal.archives-ouvertes.fr/hal-01376535

A. Szepessy, Convergence of a shock-capturing streamline diffusion finite element method for a scalar conservation law in two space dimensions, Mathematics of Computation, vol.53, issue.188, pp.527-545, 1989.
DOI : 10.1090/S0025-5718-1989-0979941-6

A. Szepessy, Convergence of a streamline diffusion finite element method for scalar conservation laws with boundary conditions, ESAIM: Mathematical Modelling and Numerical Analysis, vol.25, issue.6, pp.749-782, 1991.
DOI : 10.1051/m2an/1991250607491