H. W. Alt and E. Dibenedetto, Nonsteady flow of water and oil through inhomogeneous porous media, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.12, issue.43, pp.335-392, 1985.

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

S. [. Alt and . Luckhaus, Quasilinear elliptic-parabolic differential equations, Math. Z, vol.183, issue.3, pp.311-341, 1983.

]. T. Arb92 and . Arbogast, The existence of weak solutions to single porosity and simple dual-porosity models of two-phase incompressible flow, Nonlinear Anal, vol.19, issue.11, pp.1009-1031, 1992.

]. D. Bra01 and . Braess, Finite elements Theory, fast solvers, and applications in solid mechanics, Translated from the, 1992.

R. [. Chen and . Ewing, Fully Discrete Finite Element Analysis of Multiphase Flow in Groundwater Hydrology, SIAM Journal on Numerical Analysis, vol.34, issue.6, pp.2228-2253, 1997.
DOI : 10.1137/S0036142995290063

]. Z. Che01 and . Chen, Degenerate two-phase incompressible flow. I. Existence, uniqueness and regularity of a weak solution, J. Differential Equations, vol.171, issue.2, pp.203-232, 2001.

J. [. Chavent and . Jaffré, Mathematical models and finite elements for reservoir simulation Single phase, multiphase and multicomponent flows through porous media, Studies in Mathematics and its Applications, 1986.

L. [. Chin and . Thomas, Fully Coupled Analysis of Improved Oil Recovery by Reservoir Compaction, SPE Annual Technical Conference and Exhibition, 1999.
DOI : 10.2118/56753-MS

R. Da¨?mda¨?m, D. Eymard, R. Hilhorst, M. Masson, and . Mainguy, A Preconditioned Conjugate Gradient Based Algorithm for Coupling Geomechanical-Reservoir Simulations, Oil & Gas Science and Technology, vol.57, issue.5, pp.515-523, 2002.
DOI : 10.2516/ogst:2002034

M. [. Eymard, D. Gutnic, and . Hilhorst, The finite volume method for an elliptic-parabolic equation, Acta Math. Univ. Comen., New Ser, vol.67, issue.1, pp.181-195, 1998.

T. [. Eymard, R. Gallouët, A. Herbin, and . Michel, Convergence of a finite volume scheme for nonlinear degenerate parabolic equations, Numerische Mathematik, vol.92, issue.1, pp.41-82, 2002.
DOI : 10.1007/s002110100342

G. Gagneux and M. Madaune-tort, Analyse mathématique de modèles non linéaires de l'ingénieriepétrolì ere, Mathématiques & Applications, vol.22

]. C. Kel95 and . Kelley, Iterative methods for linear and nonlinear equations, Frontiers in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), vol.16, 1995.

O. [. Kufner, S. John, and . Fuvcík, Function spaces Monographs and Textbooks on Mechanics of Solids and Fluids, 1977.

S. [. Kroener and . Luckhaus, Flow of oil and water in a porous medium, Journal of Differential Equations, vol.55, issue.2
DOI : 10.1016/0022-0396(84)90084-6

S. [. Kruzkov and . Sukorjanskii, Boundary value problems for systems of equations of two-phase filtration type ; formulation of problems, questions of solvability, justification of approximate methods, Mat. Sb. (N.S.), vol.104, issue.1461, pp.69-88, 1977.

V. [. Ladyvzenskaja, N. N. Solonnikov, R. I. Ural-ceva, R. Lascaux, . V. Théodorpao92-]-c et al., Translated from the Russian by S Analyse numérique matricielle appliquéeappliquéè a l'art de l'ingénieur Méthodes itératives. [Iterative methods]. [Mic03] A. Michel. A finite volume scheme for two-phase immiscible flow in porous media Nonlinear parabolic and elliptic equations Application de la méthode des volumes finisàfinis`finisà des probì emes d'environnement et de traitement d'image Iterative methods for sparse linear systems, Linear and quasilinear equations of parabolic type Thèse. [Saa03] Y. SaadShe94] J. R. Shewchuk. An introduction to the conjugate gradient method without agonizing pain. Pittsburgh, 1 editionSM94] A. Settari and F.M. Mourits. Coupling of geomechanics and reservoir simulation models, pp.1301-13172151, 1967.

. E. Str-+-99-]-j, L. K. Sylte, D. W. Thomas, D. D. Rhett, N. B. Bruning et al., Water induced compaction in the ekofisk filed Advances in coupled geomechanical and reservoir modeling with applications to reservoir compaction. SPE Reservoir Simulation Symposium Theory and numerical analysis Reservoir simulation integrated with geomechanics The existence and uniqueness theorem in Biot's consolidation theory, Studies in Mathematics and its Applications, pp.28-37194, 1977.