L. Agélas, R. Eymard, and S. Lemaire, Convergence of Euler-Gradient approximations of Biot's consolidation problem on general meshes, 2014.

G. Aguilar, F. Gaspar, F. Lisbona, and C. Rodrigo, Numerical stabilization of Biot's consolidation model by a perturbation on the flow equation, International Journal for Numerical Methods in Engineering, vol.1, issue.11, pp.1282-1300, 2008.
DOI : 10.1002/nme.2295

G. Allaire, Analyse numérique et optimisation. Les éditions de l'École Polytechnique, 2009.

D. N. Arnold, F. Brezzi, and J. Douglas, PEERS: A new mixed finite element for plane elasticity, Japan Journal of Applied Mathematics, vol.41, issue.2, pp.347-367, 1984.
DOI : 10.1007/BF03167064

J. Auriault and E. Sanchez-palencia, Étude du comportement macroscopique d'un milieu poreux saturé déformable, Journal de Mécanique, vol.16, pp.576-603, 1977.

F. Auricchio, L. Beirão-da-veiga, A. Buffa, C. Lovadina, A. Reali et al., A fully ???locking-free??? isogeometric approach for plane linear elasticity problems: A stream function formulation, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.1-4, pp.1-4160, 2007.
DOI : 10.1016/j.cma.2007.07.005

L. Beirão and . Veiga, A mimetic discretization method for linear elasticity, ESAIM: Mathematical Modelling and Numerical Analysis, vol.44, issue.2, pp.231-250, 2010.
DOI : 10.1051/m2an/2010001

L. Beirão-da-veiga, F. Brezzi, and L. D. Marini, Virtual Elements for Linear Elasticity Problems, SIAM Journal on Numerical Analysis, vol.51, issue.2, pp.794-812, 2013.
DOI : 10.1137/120874746

L. Beirão-da-veiga, V. Gyrya, K. Lipnikov, and G. Manzini, Mimetic finite difference method for the Stokes problem on polygonal meshes, Journal of Computational Physics, vol.228, issue.19, pp.7215-7232, 2009.
DOI : 10.1016/j.jcp.2009.06.034

L. Beirão-da-veiga, K. Lipnikov, and G. Manzini, Error Analysis for a Mimetic Discretization of the Steady Stokes Problem on Polyhedral Meshes, SIAM Journal on Numerical Analysis, vol.48, issue.4, pp.1419-1443, 2010.
DOI : 10.1137/090757411

J. Haga, H. Osnes, and H. P. Langtangen, On the causes of pressure oscillations in low-permeable and low-compressible porous media, International Journal for Numerical and Analytical Methods in Geomechanics, vol.143, issue.4, pp.1507-1522, 2012.
DOI : 10.1002/nag.1062

M. A. Biot, General Theory of Three???Dimensional Consolidation, Journal of Applied Physics, vol.12, issue.2, pp.155-164, 1941.
DOI : 10.1063/1.1712886
URL : https://hal.archives-ouvertes.fr/hal-01368635

F. Boyer, S. Krell, and F. Nabet, Inf-sup stability of the Discrete Duality Finite Volume method for the 2D Stokes problem. 2013. Submitted. Preprint available at http
URL : https://hal.archives-ouvertes.fr/hal-00795362

S. C. Brenner, Korn's inequalities for piecewise $H^1$ vector fields, Mathematics of Computation, vol.73, issue.247, pp.1067-1087, 2004.
DOI : 10.1090/S0025-5718-03-01579-5

S. C. Brenner and L. R. Scott, The mathematical theory of finite element methods, Texts in Applied Mathematics, vol.15, 2008.

S. C. Brenner and L. Sung, Linear finite element methods for planar linear elasticity, Mathematics of Computation, vol.59, issue.200, pp.321-338, 1992.
DOI : 10.1090/S0025-5718-1992-1140646-2

F. Brezzi and M. Fortin, Mixed and hybrid finite element methods, of Springer Series in Computational Mathematics, 1991.
DOI : 10.1007/978-1-4612-3172-1

F. Brezzi, K. Lipnikov, and M. Shashkov, Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes, SIAM Journal on Numerical Analysis, vol.43, issue.5, pp.1872-1896, 2005.
DOI : 10.1137/040613950

F. Brezzi, K. Lipnikov, M. Shashkov, and V. Simoncini, A new discretization methodology for diffusion problems on generalized polyhedral meshes, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.37-40, pp.37-403682, 2007.
DOI : 10.1016/j.cma.2006.10.028

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.15, issue.10, pp.151533-1551, 2005.
DOI : 10.1142/S0218202505000832

K. S. Chavan, B. P. Lamichhane, and B. I. Wohlmuth, Locking-free finite element methods for linear and nonlinear elasticity in 2D and 3D, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.41-44, pp.4075-4086, 2007.
DOI : 10.1016/j.cma.2007.03.022

M. Crouzeix and P. Raviart, Conforming and nonconforming finite element methods for solving the stationary Stokes equations I, Revue fran??aise d'automatique informatique recherche op??rationnelle. Math??matique, vol.7, issue.R3, pp.33-75, 1973.
DOI : 10.1051/m2an/197307R300331

D. A. Di-pietro, Cell centered Galerkin methods for diffusive problems, ESAIM: Mathematical Modelling and Numerical Analysis, vol.46, issue.1, pp.111-144, 2012.
DOI : 10.1051/m2an/2011016
URL : https://hal.archives-ouvertes.fr/hal-00511125

D. A. Di-pietro and A. Ern, Mathematical aspects of discontinuous Galerkin methods, of Mathématiques & Applications, 2011.
DOI : 10.1007/978-3-642-22980-0

D. A. Di-pietro, R. Eymard, S. Lemaire, and R. Masson, Hybrid Finite Volume Discretization of Linear Elasticity Models on General Meshes, Finite Volumes for Complex Applications VI Problems & Perspectives, pp.331-339, 2011.
DOI : 10.1007/978-3-642-20671-9_35
URL : https://hal.archives-ouvertes.fr/hal-00795201

D. A. Di-pietro and J. Gratien, Lowest order methods for diffusive problems on general meshes: A unified approach to definition and implementation, Finite Volumes for Complex Applications VI Problems & Perspectives, pp.803-819, 2011.
DOI : 10.1007/978-3-642-20671-9_84
URL : https://hal.archives-ouvertes.fr/hal-00562500

D. A. Di-pietro, J. Gratien, and C. , A domain-specific embedded language in C++ for lowest-order discretizations of diffusive problems on general meshes, BIT Numerical Mathematics, vol.14, issue.2, pp.111-152, 2013.
DOI : 10.1007/s10543-012-0403-3
URL : https://hal.archives-ouvertes.fr/hal-00654406

D. A. Di-pietro and S. Lemaire, An extension of the Crouzeix?Raviart space to general meshes with application to quasi-incompressible linear elasticity and Stokes flow Accepted for publication, Math. Comp, 2013.

D. A. Di-pietro and S. Nicaise, A locking-free discontinuous Galerkin method for linear elasticity in locally nearly incompressible heterogeneous media, Applied Numerical Mathematics, vol.63, pp.105-116, 2013.
DOI : 10.1016/j.apnum.2012.09.009
URL : https://hal.archives-ouvertes.fr/hal-00685020

J. Droniou and R. Eymard, A mixed finite volume scheme for anisotropic diffusion problems on any grid, Numerische Mathematik, vol.59, issue.1, pp.35-71, 2006.
DOI : 10.1007/s00211-006-0034-1
URL : https://hal.archives-ouvertes.fr/hal-00005565

J. Droniou and R. Eymard, Study of the mixed finite volume method for Stokes and Navier-Stokes equations, Numerical Methods for Partial Differential Equations, vol.7, issue.1, pp.137-171, 2009.
DOI : 10.1002/num.20333
URL : https://hal.archives-ouvertes.fr/hal-00110911

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.20, issue.02
DOI : 10.1142/S0218202510004222
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, M3AS), pp.2395-2432, 2013.
DOI : 10.1142/S0218202513500358
URL : https://hal.archives-ouvertes.fr/hal-00751551

T. Dupont and R. Scott, Polynomial approximation of functions in Sobolev spaces, Mathematics of Computation, vol.34, issue.150, pp.441-463, 1980.
DOI : 10.1090/S0025-5718-1980-0559195-7

A. Ern and J. Guermond, Theory and practice of finite elements, Applied Mathematical Sciences, vol.159, 2004.
DOI : 10.1007/978-1-4757-4355-5

A. Ern and S. Meunier, error analysis of Euler-Galerkin approximations to coupled elliptic-parabolic problems, ESAIM: Mathematical Modelling and Numerical Analysis, vol.43, issue.2, pp.353-375, 2009.
DOI : 10.1051/m2an:2008048
URL : https://hal.archives-ouvertes.fr/hal-00164851

R. Eymard, P. Féron, T. Gallouët, C. Guichard, and R. Herbin, Gradient schemes for the Stefan problem, Int. J. Finite, vol.10, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00751555

R. Eymard, T. Gallouët, and R. Herbin, The finite volume method, volume 7 of Handbook of Numerical Analysis, 2000.

R. Eymard, T. Gallouët, and R. Herbin, A new finite volume scheme for anisotropic diffusion problems on general grids: convergence analysis, Comptes Rendus Mathematique, vol.344, issue.6, pp.403-406, 2007.
DOI : 10.1016/j.crma.2007.01.024

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.46, issue.2, pp.265-290, 2012.
DOI : 10.1051/m2an/2011040
URL : https://hal.archives-ouvertes.fr/hal-00542667

R. Eymard, C. Guichard, R. Herbin, and R. Masson, Multiphase Flow in Porous Media Using the VAG Scheme, Finite Volumes for Complex Applications VI Problems & Perspectives, pp.409-417, 2011.
DOI : 10.1007/978-3-642-20671-9_43
URL : https://hal.archives-ouvertes.fr/hal-01238557

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 : 10.1007/s10596-012-9299-x
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, 2013.
DOI : 10.1002/zamm.201200206
URL : https://hal.archives-ouvertes.fr/hal-00740367

R. Eymard and R. Herbin, Gradient Scheme Approximations for Diffusion Problems, Finite Volumes for Complex Applications VI Problems & Perspectives, pp.439-447, 2011.
DOI : 10.1007/978-3-642-20671-9_46

R. S. Falk, Nonconforming finite element methods for the equations of linear elasticity, Mathematics of Computation, vol.57, issue.196, pp.529-550, 1991.
DOI : 10.1090/S0025-5718-1991-1094947-6

K. J. Galvin, A. Linke, L. G. Rebholz, and N. E. Wilson, Stabilizing poor mass conservation in incompressible flow problems with large irrotational forcing and application to thermal convection, Computer Methods in Applied Mechanics and Engineering, vol.237, issue.240, pp.237-240166, 2012.
DOI : 10.1016/j.cma.2012.05.008

V. Girault and P. Raviart, Finite element methods for Navier?Stokes equations Theory and algorithms, of Springer Series in Computational Mathematics, 1986.

P. Hansbo and M. G. Larson, Discontinuous Galerkin methods for incompressible and nearly incompressible elasticity by Nitsche's method, Computer Methods in Applied Mechanics and Engineering, vol.191, issue.17-18, pp.17-181895, 2002.
DOI : 10.1016/S0045-7825(01)00358-9

P. Hansbo and M. G. Larson, Discontinuous Galerkin and the Crouzeix???Raviart element: Application to elasticity, ESAIM: Mathematical Modelling and Numerical Analysis, vol.37, issue.1, pp.63-72, 2003.
DOI : 10.1051/m2an:2003020

J. G. Heywood and R. Rannacher, Finite-Element Approximation of the Nonstationary Navier???Stokes Problem. Part IV: Error Analysis for Second-Order Time Discretization, SIAM Journal on Numerical Analysis, vol.27, issue.2, pp.353-384, 1990.
DOI : 10.1137/0727022

J. Kim, H. A. Tchelepi, and R. Juanes, Stability, Accuracy, and Efficiency of Sequential Methods for Coupled Flow and Geomechanics, SPE Journal, vol.16, issue.02, pp.249-262, 2011.
DOI : 10.2118/119084-PA

J. Korsawe and G. Starke, A Least-Squares Mixed Finite Element Method for Biot's Consolidation Problem in Porous Media, SIAM Journal on Numerical Analysis, vol.43, issue.1, pp.318-339, 2005.
DOI : 10.1137/S0036142903432929

J. Korsawe, G. Starke, W. Wang, and O. Kolditz, Finite element analysis of poro-elastic consolidation in porous media: Standard and mixed approaches, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.9-12, pp.9-121096, 2006.
DOI : 10.1016/j.cma.2005.04.011

S. Krell and G. Manzini, The Discrete Duality Finite Volume Method for Stokes Equations on Three-Dimensional Polyhedral Meshes, SIAM Journal on Numerical Analysis, vol.50, issue.2, pp.808-837, 2012.
DOI : 10.1137/110831593

B. P. Lamichhane and E. P. Stephan, A symmetric mixed finite element method for nearly incompressible elasticity based on biorthogonal systems, Numerical Methods for Partial Differential Equations, vol.8, issue.4, pp.1336-1353, 2012.
DOI : 10.1002/num.20683

K. Mahesh, G. Constantinescu, and P. Moin, A numerical method for large-eddy simulation in complex geometries, Journal of Computational Physics, vol.197, issue.1, pp.215-240, 2004.
DOI : 10.1016/j.jcp.2003.11.031

A. Mikeli? and M. F. Wheeler, Convergence of iterative coupling for coupled flow and geomechanics, Computational Geosciences, vol.3, issue.3, pp.455-462, 2013.
DOI : 10.1007/s10596-012-9318-y

M. A. Murad and A. F. Loula, Improved accuracy in finite element analysis of Biot's consolidation problem, Computer Methods in Applied Mechanics and Engineering, vol.95, issue.3, pp.359-382, 1992.
DOI : 10.1016/0045-7825(92)90193-N

M. A. Murad and A. F. Loula, On stability and convergence of finite element approximations of Biot's consolidation problem, International Journal for Numerical Methods in Engineering, vol.1, issue.4, pp.645-667, 1994.
DOI : 10.1002/nme.1620370407

M. A. Murad, V. Thomée, and A. F. Loula, Asymptotic Behavior of Semidiscrete Finite-Element Approximations of Biot???s Consolidation Problem, SIAM Journal on Numerical Analysis, vol.33, issue.3, pp.1065-1083, 1996.
DOI : 10.1137/0733052

J. Ne?as, Équations aux dérivées partielles. Les Presses de l, 1966.

J. M. Nordbotten, Cell-centered finite volume discretizations for deformable porous media, International Journal for Numerical Methods in Engineering, vol.246, issue.3, 2013.
DOI : 10.1002/nme.4734

P. J. Phillips and M. F. Wheeler, A coupling of mixed and continuous Galerkin finite element methods for poroelasticity I: the continuous in time case, Computational Geosciences, vol.29, issue.2, pp.131-144, 2007.
DOI : 10.1007/s10596-007-9045-y

P. J. Phillips and M. F. Wheeler, A coupling of mixed and continuous Galerkin finite element methods for poroelasticity II: the discrete-in-time case, Computational Geosciences, vol.10, issue.2, pp.145-158, 2007.
DOI : 10.1007/s10596-007-9044-z

P. J. Phillips and M. F. Wheeler, A coupling of mixed and discontinuous Galerkin finite-element methods for poroelasticity, Computational Geosciences, vol.29, issue.2, pp.417-435, 2008.
DOI : 10.1007/s10596-008-9082-1

P. J. Phillips and M. F. Wheeler, Overcoming the problem of locking in linear elasticity and poroelasticity: an heuristic approach, Computational Geosciences, vol.11, issue.1871, pp.5-12, 2009.
DOI : 10.1007/s10596-008-9114-x

D. K. Ponting, Corner Point Geometry in Reservoir Simulation, ECMOR I, 1st European Conference on the Mathematics of Oil Recovery, pp.45-65, 1989.
DOI : 10.3997/2214-4609.201411305

A. Quarteroni and A. Valli, Numerical approximation of partial differential equations, of Springer Series in Computational Mathematics, 1994.

R. Rannacher and S. Turek, Simple nonconforming quadrilateral Stokes element, Numerical Methods for Partial Differential Equations, vol.2, issue.2, pp.97-111, 1992.
DOI : 10.1002/num.1690080202

A. Settari and F. M. Mourits, Coupling of geomechanics and reservoir simulation models, In Comput. Methods Adv. Geomech, pp.2151-2158, 1994.

G. Shaw and T. Stone, Finite Volume Methods for Coupled Stress/Fluid Flow in a Commercial Reservoir Simulator, SPE Reservoir Simulation Symposium, 2005.
DOI : 10.2118/93430-MS

R. E. Showalter, Diffusion in Poro-Elastic Media, Journal of Mathematical Analysis and Applications, vol.251, issue.1, pp.310-340, 2000.
DOI : 10.1006/jmaa.2000.7048

R. Stenberg, A family of mixed finite elements for the elasticity problem, Numerische Mathematik, vol.3, issue.5, pp.513-538, 1988.
DOI : 10.1007/BF01397550

G. Strang, Variational crimes in the finite element method The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, 1972.

A. T. Eyck and A. Lew, Discontinuous Galerkin methods for non-linear elasticity, International Journal for Numerical Methods in Engineering, vol.60, issue.9, pp.1204-1243, 2006.
DOI : 10.1002/nme.1667

M. Vogelius, An analysis of thep-version of the finite element method for nearly incompressible materials, Numerische Mathematik, vol.5, issue.1, pp.39-53, 1983.
DOI : 10.1007/BF01396304

M. Vohralík and B. I. Wohlmuth, From face to element unknowns by local static condensation with application to nonconforming finite elements, Computer Methods in Applied Mechanics and Engineering, vol.253, pp.517-529, 2013.
DOI : 10.1016/j.cma.2012.08.013

M. Vohralík and B. I. Wohlmuth, MIXED FINITE ELEMENT METHODS: IMPLEMENTATION WITH ONE UNKNOWN PER ELEMENT, LOCAL FLUX EXPRESSIONS, POSITIVITY, POLYGONAL MESHES, AND RELATIONS TO OTHER METHODS, M3AS), pp.803-838, 2013.
DOI : 10.1142/S0218202512500613

K. Terzaghi, Theoretical soil mechanics, J. Wiley and Sons, 1943.
DOI : 10.1002/9780470172766

A. ?ení?ek, The existence and uniqueness theorem in Biot's consolidation theory, Aplik. Matem, vol.29, issue.3, pp.194-211, 1984.

J. Wan, L. J. Durlofsky, T. J. Hughes, and K. Aziz, Stabilized Finite Element Methods for Coupled Geomechanics - Reservoir Flow Simulations, SPE Reservoir Simulation Symposium, 2003.
DOI : 10.2118/79694-MS

M. F. Wheeler, G. Xue, and I. Yotov, Coupling multipoint flux mixed finite element methodswith continuous Galerkin methods for poroelasticity, Computational Geosciences, vol.121, issue.1, 2013.
DOI : 10.1007/s10596-013-9382-y

J. P. Whiteley, Discontinuous Galerkin finite element methods for incompressible nonlinear elasticity, Comput. Methods Appl. Mech. Engrg, vol.198, pp.41-443464, 2009.