An introduction to multipoint ux approximations for quadrilateral grids, Computational Geosciences, vol.6, p.405432, 2002. ,
Discretization on Unstructured Grids for Inhomogeneous, Anisotropic Media. Part I: Derivation of the Methods, SIAM Journal on Scientific Computing, vol.19, issue.5, p.17001716, 1998. ,
DOI : 10.1137/S1064827595293582
Discretization on Unstructured Grids For Inhomogeneous, Anisotropic Media. Part II: Discussion And Numerical Results, SIAM Journal on Scientific Computing, vol.19, issue.5, p.17171736, 1998. ,
DOI : 10.1137/S1064827595293594
On convergence of nite volume schemes for a degenerate convection-diusion equation arising in ow in porous media, Comput. Methods Appl. Mech. Engrg, vol.191, p.52655286, 2002. ,
Nonsteady ow of water and oil through inhomogeneous porous media, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.12, issue.43, p.335392, 1985. ,
On nonstationary ow through porous media, Ann. Mat. Pura Appl, vol.136, issue.4, p.303316, 1984. ,
A new formulation of immiscible compressible twophase ow in porous media, Comptes Rendus Mécanique, vol.336, issue.7, p.600605, 2008. ,
Discrete duality nite volume schemes for doubly nonlinear degenerate hyperbolic-parabolic equations, J. Hyperbolic Di. Equ, vol.7, issue.1, p.167, 2010. ,
A nite volume method on general meshes for a degenerate parabolic convection-reaction-diusion equation, 2011. ,
A nite volume scheme for diusion problems on general meshes applying monotony constraints, SIAM J. Numer. Anal, vol.47, p.41934213, 2010. ,
Finite volume approximation of a diusion-dissolution model and application to nuclear waste storage, J. Math. and Comp. in Sim, issue.10, p.81, 2011. ,
Analysis of a combined barycentric nite volume -nonconforming nite element method for nonlinear convection -diusion problem, Applications of Mathematics, vol.43, p.263310, 1998. ,
Boundary value problems in mechanics of nonhomogeneous uids, Studies in Mathematics and its Applications, 1990. ,
The existence of weak solutions to single porosity and simple dual porosity models of twophase incompressible ow. Nonlinear Anal, Theory Methods Appl, vol.19, p.10091031, 1992. ,
A nonlinear mixed nite element method for a degenerate parabolic equation arising in ow in porous media, SIAM J. Numer. Anal, vol.33, p.16691687, 1996. ,
Discontinuous galerkin methods for two-phase ow in porous media, 2004. ,
Co-volume methods for degenerate parabolic problems, Numerische Mathematik, vol.14, issue.1, p.4567, 1993. ,
DOI : 10.1007/BF01388680
Dynamics of uids in porous media, 1972. ,
Modeling groundwater ow and pollution. Reidel, 1987. ,
Convergence of mimetic nite dierence discretizations of the diusion equation, EastWest J. Numer. Math, vol.9, p.253284, 2001. ,
Analysis of oil trapping in porous media ow, SIAM J. Math. Anal, vol.35, issue.1, p.245267, 2003. ,
Hybrid nite volume scheme for a two-phase ow problem ,
A convergent nite volume scheme for two-phase ows in porous media with discontinuous capillary pressure eld. Finite Volumes for Complex App, p.185194, 2011. ,
Analyse Fonctionnelle : Théorie et applications, 1983. ,
Mimetic nite dierences for elliptic problems, Math. Mod. Numer. Anal, vol.43, p.277295, 2009. ,
Mixed and Hybrid Finite Element Methods, 1991. ,
DOI : 10.1007/978-1-4612-3172-1
Convergence of the mimetic nite dierence method for diusion problems on polyhedral meshes, SIAM J. Numer. Anal, vol.43, issue.5, p.18721896, 2005. ,
A new discretization methodology for diusion problems on generalized polyhedral meshes, Comput. Methods Appl. Mech. Engrg, vol.196, p.36823692, 2007. ,
A family of mimetic nite dierence methods on polygonal and polyhedral meshes, Math. Models Methods Appl. Sci, vol.15, issue.10, p.15331551, 2005. ,
Interface conditions for degenerate two-phase ow equations in one space dimension, Analysis, vol.29, issue.3, p.299316, 2009. ,
Nonlinear parabolic equations with spatial discontinuities, NoDEA Nonlinear Dierential Equations Appl, vol.15, issue.4-5, p.427456, 2008. ,
Asymptotic behavior of two-phase ows in heterogeneous porous media for capillarity depending only on space. i. convergence to the optimal entropy solution [36] C. Cancès. Asymptotic behavior of two-phase ows in heterogeneous porous media for capillarity depending only on space. ii. non-classical shocks to model oiltrapping, SIAM J. Math. Anal. SIAM J. Math. Anal, vol.42, issue.422, p.946971972995, 2010. ,
On the eects of discontinuous capillarities for immiscible twophase ows in porous media made of several rock-types. Paper of the conference NTMC09, to appear in Networks and heterogeneous media, 2010. ,
An existence result for multidimensional immiscible two-phase ows with discontinuous capillary pressure eld, 2010. ,
Écoulement diphasiques en milieux poreux hétérogènes : modélisation et analyse, Thèse de doctorat, 2008. ,
Finite volume scheme for two-phase ow in heterogeneous porous media involving capillary pressure discontinuities, p.9731001, 2009. ,
Two-phase ows involving capillary barriers in heterogeneous porous media. Interfaces and Free Bound, pp.239-258, 2009. ,
Convergence analysis of a mimetic nite dierence method for general secondorder elliptic problems, SIAM J. Numer. Anal, vol.47, issue.4, p.26122637, 2009. ,
Convergence analysis of a mixed nite volume scheme for an ellipticparabolic system modeling miscible uid ows in porous media, SIAM J. Numer. Anal, vol.45, issue.5, p.22282258, 2007. ,
Mathematical models and nite elements for reservoir simulation, 1986. ,
Degenerate two-phase incompressible ow. I. Existence, uniqueness and regularity of a weak solution, J. Dierential Equations, vol.171, issue.2, p.203232, 2001. ,
DOI : 10.1006/jdeq.2000.3848
URL : http://doi.org/10.1006/jdeq.2000.3848
Fullydiscrete nite element analysis of multiphase ow in groundwater hydrology, SIAM J. Num . Anal, vol.34, p.22282253, 1997. ,
Error analysis for characteristicsbased methods for degenerate parabolic problems, SIAM J. Numer. Anal, vol.40, p.14911515, 2002. ,
Degenerate two-phase incompressible ow. III. Sharp error estimates, Numer. Math, vol.90, issue.2, p.215240, 2001. ,
DOI : 10.1006/jdeq.2000.3848
URL : http://doi.org/10.1006/jdeq.2000.3848
Computational methods for multiphase ows in porous media, SIAM, 2006. ,
Degenerate two-phase incompressible ow problems. I. Regularization and numerical results, Commun. Appl. Anal, vol.5, issue.3, p.319334, 2001. ,
DOI : 10.1006/jdeq.2000.3848
URL : http://doi.org/10.1006/jdeq.2000.3848
Degenerate two-phase incompressible ow problems. II. Error estimates, Commun. Appl. Anal, vol.5, issue.4, p.503521, 2001. ,
DOI : 10.1006/jdeq.2000.3848
URL : http://doi.org/10.1006/jdeq.2000.3848
Convergence rate of a nite volume scheme for a two dimensional diusion convection problem, M2AN Math. Model. Numer. Anal, vol.33, p.493516, 1999. ,
Analysis of an upwind-mixed nite element method for nonlinear contaminant transport equations, SIAM J. Numer. Anal, vol.35, p.17091724, 1998. ,
Upwind mixed methods for transport equations, Comput. Geosci, vol.3, p.93110, 1999. ,
Nonlinear Functional Analysis, 1985. ,
DOI : 10.1007/978-3-662-00547-7
Remarks on discretizations of convection terms in Hybrid mimetic mixed methods, Networks and Heterogeneous Media, vol.5, issue.3, 2010. ,
DOI : 10.3934/nhm.2010.5.545
Study of the mixed nite volume method for stokes and navierstokes equations, Numer. Meth. P. D. E, vol.25, issue.1, p.137171, 2009. ,
A unied approach to mimetic nite dierence, hybrid nite volume and mixed nite volume methods ,
The eect of capillary forces on immiscible two-phase ow in heterogeneous porous media, Transport in Porous Media, p.7193, 1995. ,
Numerical approximation of a two-phase ow in a porous medium with discontinuous capillary forces, SIAM J. Numer. Anal, vol.43, issue.6, p.24022422, 2006. ,
Discontinuous galerkin approximation of two-phase ows in heterogeneous porous media with discontinuous capillary pressures, CERMICS Research Report, vol.398, 2009. ,
Numerical methods for ow in a porous medium with internal boundaries, Comput. Geosci, vol.2, issue.3, p.217240, 1998. ,
Mixed nite element approximation of phase velocities in compositional reservoir simulation, Comput. Methods Appl. Mech. Engrg. (R.E. Ewing, p.47161176, 1984. ,
Galerkin methods for miscible displacement problems with point sources and sinksunit mobility ratio, Mathematical Methods in Energy Research, p.4059, 1983. ,
Finite Volume Methods, Handbook of Numerical Analysis, Lions eds, 2000. ,
Discretization of heterogeneous and anisotropic diusion problems on general nonconforming meshes sushi : a scheme using stabilization and hybrid interfaces, IMA J. of Num. Anal, vol.30, issue.4, p.10091043, 2010. ,
Convergence of a nite volume scheme for nonlinear degenerate parabolic equations, Numer. Math, vol.92, p.4182, 2002. ,
Finite volumes and nonlinear diusion equations, M2AN Math. Model. Numer. Anal, vol.32, p.747761, 1998. ,
The nite volume method for the richards equation, Comput. Geosci, vol.3, p.259294, 2000. ,
3d benchmark on discretization schemes for anisotropic diusion problems on general grids. Finite Volumes for Complex App Mathematical study of a petroleumengineering scheme, Math. Mod. Numer. Anal, vol.2, issue.376, p.95130937972, 2003. ,
A combined nite volume nonconforming/mixed-hybrid nite element scheme for degenerate parabolic problems, Numer. Math, vol.105, p.73131, 2006. ,
A combined nite volume-nite element scheme for the discretization of strongly nonlinear convection-diusion-reaction problems on nonmatching grids, Numer. Methods for Partial Dier. Equations, vol.26, p.612646, 2009. ,
On the convergence of a combined nite volume-nite element method for nonlinear convection-diusion problems, Numer. Methods for Partial Dier. Equations, vol.13, p.163190, 1997. ,
Hyperbolic equations and systems with discontinuous coecients or source terms, Proceedings of Equadi-11, 2005. ,
Discrete sobolev-poincaré inequalities for voronoi nite volume approximations, SIAM J. Numer. Anal, vol.48, p.24892513, 2010. ,
Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries, Advances in Water Resources, vol.13, issue.4, pp.169-186, 1990. ,
DOI : 10.1016/0309-1708(90)90040-B
Thermodynamic basis of capillary pressure in porous media, Water Resources Research, vol.29, issue.1, p.33893405, 1993. ,
DOI : 10.1029/93WR01495
Benchmark on discretization schemes for anisotropic diffusion problems on general grids for anisotropic heterogeneous diusion problems. Finite Volumes for Complex App, p.659692, 2008. ,
Operator splitting methods for degenerate convection-diusion equations ii : Numerical examples with emphasis on reservoir simulation and sedimentation, Computational Geosciences, 2000. ,
Mimetic nite dierence methods for the diusion equation, Comput. Geosci, vol.6, p.333352, 2002. ,
Numerical calculation of the ux across an interface between two rock types of a porous medium for a two-phase ow Hyperbolic Problems : Theory, Numerics, Applications, p.165177, 1996. ,
Upwind dierence approximations for degenerate parabolic convection-diusion equations with a discontinuous coecient, IMA J. Numer. Anal, vol.22, p.623664, 2002. ,
Solution of degenerate convection-diusion problems by the method of characteristics, SIAM J. Numer. Anal, vol.39, p.858879, 2001. ,
Solution of contaminant transport with adsorption in porous media by the method of characteristics, ESAIM : M2AN Math. Model. Numer. Anal, vol.35, p.9811006, 2001. ,
Solute transport in porous media with equilibrium and nonequilibrium multiple-site adsorption: uniqueness of weak solutions, Nonlinear Analysis: Theory, Methods & Applications, vol.42, issue.3, p.381403, 2000. ,
DOI : 10.1016/S0362-546X(98)00352-6
A nine-point nite volume scheme for the simulation of diusion in heterogeneous media, Comptes Rendus Mathématique, vol.347, issue.11, p.12673676, 2009. ,
Local ux mimetic nite dierence methods, Numer. Math, vol.112, p.115152, 2009. ,
DOI : 10.1007/s00211-008-0203-5
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.139.7602
Flux reconstruction and pressure postprocessing in mimetic nite dierence methods, Comput. Methods Appl. Mech. Engrg, vol.197, pp.9-12933, 2008. ,
A nite volume scheme for two-phase immiscible ow in porous media, SIAM J. Numer. Anal, vol.41, issue.4, p.13011317, 2003. ,
Nonlinear nite volume method for two phase ow in porous media, Math. Model, vol.20, issue.11, p.131147, 2010. ,
Approximation of Degenerate Parabolic Problems Using Numerical Integration, SIAM Journal on Numerical Analysis, vol.25, issue.4, p.784814, 1988. ,
DOI : 10.1137/0725046
A posteriori error estimation and adaptivity for degenerate parabolic
problems, Mathematics of Computation, vol.69, issue.229, p.124, 2000. ,
DOI : 10.1090/S0025-5718-99-01097-2
Convergence of a mixed nite element -nite volume method for the two phase ow in porous media, East-West J. Numer. Math, vol.5, issue.3, p.183210, 1997. ,
Macroscopic equations derived from space averaging for immiscible two-phase ow in porous media, pp.29-41, 1989. ,
Fundamentals of Numerical Reservoir Simulation, 1977. ,
Convergence of a Discontinuous Galerkin Method for the Miscible Displacement Equation under Low Regularity, SIAM Journal on Numerical Analysis, vol.49, issue.3 ,
DOI : 10.1137/090758908
Optimal Rates of Convergence for Degenerate Parabolic Problems in Two Dimensions, SIAM Journal on Numerical Analysis, vol.33, issue.1, p.5667, 1996. ,
DOI : 10.1137/0733004
Analysis and approximation of a scalar conservation law with a ux function with discontinuous coecient, p.221257, 2003. ,
Convergence of a dierence scheme for conservation laws with a discontinuous ux, SIAM J. Numer. Anal, vol.38, issue.2, p.681698, 2000. ,
A unied approach for handling convection terms in nite volumes and mimetic discretization methods for elliptic problems, IMA J. Numer. Anal, p.145, 2010. ,
Convergence analysis of the highorder mimetic nite dierence method, Numer. Math, vol.113, issue.3, p.325356, 2009. ,
An a posteriori error estimator for the mimetic nite dierence approximation of elliptic problems, Int. J. for Numer. Meth. in Engnr, issue.11, p.7616961723, 2008. ,
A higherorder formulation of the mimetic nite dierence method, SIAM J. Sci. Comput, vol.31, issue.1, p.732760, 2008. ,