G. Chavent and J. Jaffre, Mathematical Models and Finite Elements for Reservoir Simulation, vol.17, 1986.

F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, 1991.

P. Raviart and J. Thomas, A mixed finite element method for second order elliptic problems, Mathematical Aspects of Finite Element Method, Lecture Notes in Mathematics, vol.606, pp.292-315, 1977.

D. Arnold and F. Brezzi, Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates, RAIRO Modél. Math. Anal. Numér, vol.19, issue.1, pp.7-32, 1985.

V. Fontaine and A. Younes, Computational issues of hybrid and multipoint mixed methods for groundwater flow in anisotropic media, Comput. Geosci, vol.14, issue.1, pp.171-181, 2010.
URL : https://hal.archives-ouvertes.fr/insu-00578745

D. Arnold, F. Brezzi, B. Cockburn, and L. Marini, Unified analysis of discontinuous Galerkin methods for elliptic problems, SIAM J. Numer. Anal, vol.39, issue.5, pp.1749-1779, 2002.

R. M. Kirby, S. J. Sherwin, and B. Cockburn, To cg or to HDG: A comparative study, J. Sci. Comput, vol.51, issue.1, pp.183-212, 2012.

B. Cockburn, W. Qiu, and K. Shi, Conditions for superconvergence of HDG methods for second-order elliptic problems, Math. Comput, vol.81, issue.279, pp.1327-1353, 2012.

B. Cockburn and J. Gopalakrishnan, A characterization of hybridized mixed methods for second order elliptic problems, SIAM J. Numer. Anal, vol.42, issue.1, pp.283-301, 2004.

B. Cockburn, J. Gopalakrishnan, and R. Lazarov, Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems, SIAM J. Numer. Anal, vol.47, issue.2, pp.1319-1365, 2009.

B. Cockburn, B. Dong, and J. Guzmán, A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems, Math. Comput, vol.77, issue.264, pp.1887-1916, 2008.

B. Cockburn, Static Condensation, Hybridization, and the Devising of the HDG Methods, pp.129-177, 2016.

D. Boffi and D. D. Pietro, Unified formulation and analysis of mixed and primal discontinuous skeletal methods on polytopal meshes, ESAIM: M2AN, vol.52, issue.1, pp.1-28, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01365938

D. D. Pietro, J. Droniou, and G. Manzini, Discontinuous skeletal gradient discretisation methods on polytopal meshes, J. Comput. Phys, vol.355, pp.397-425, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01564598

B. Cockburn, D. D. Pietro, and A. Ern, Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods, vol.50, pp.635-650, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01115318

D. D. Pietro, A. Ern, and S. Lemaire, A Review of Hybrid High-Order Methods: Formulations, Computational Aspects, Comparison with Other Methods, pp.205-236, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01163569

I. Oikawa, A hybridized discontinuous Galerkin method with reduced stabilization, J. Sci. Comput, vol.65, issue.1, pp.327-340, 2015.

C. Lehrenfeld, Hybrid Discontinuous Galerkin methods for incompressible flow problems, Diploma thesis, Rheinisch-Westfälischen Technischen Hochschule Aachen, 2010.

N. Nguyen, J. Peraire, and B. Cockburn, A hybridizable discontinuous Galerkin method for stokes flow, vol.199, pp.582-597, 2010.

N. Nguyen, J. Peraire, and B. Cockburn, An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations, J. Comput. Phys, vol.230, issue.4, pp.1147-1170, 2011.

W. Qiu and K. Shi, An HDG method for convection diffusion equation, J. Sci. Comput, vol.66, issue.1, pp.346-357, 2016.

S. Rhebergen and G. N. Wells, A hybridizable discontinuous Galerkin method for the Navier-Stokes equations with pointwise divergence-free velocity field, J. Sci. Comput, vol.76, issue.3, pp.1484-1501, 2018.

C. Lehrenfeld and J. Schöberl, High order exactly divergence-free hybrid discontinuous Galerkin methods for unsteady incompressible flows, Comput. Methods Appl. Mech. Eng, vol.307, pp.339-361, 2016.

N. Nguyen, J. Peraire, and B. Cockburn, An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations, J. Comput. Phys, vol.228, issue.9, pp.3232-3254, 2009.

D. D. Pietro and A. Ern, Hybrid High-Order methods for variable diffusion problems on general meshes, Comptes Rendus Mathématique, vol.353, pp.31-34, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01023302

P. L. Lederer, C. Lehrenfeld, and J. Schöberl, Hybrid discontinuous Galerkin methods with relaxed H(div)-conformity for incompressible flows. part i, SIAM J. Numer. Anal, vol.56, pp.2070-2094, 2018.

P. L. Lederer, C. Lehrenfeld, and J. Schöberl, Hybrid discontinuous Galerkin methods with relaxed H(div)-conformity for incompressible flows. part ii, 2018.

T. A. Davis, Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms), 2006.

A. Samii, C. Michoski, and C. Dawson, A parallel and adaptive hybridized discontinuous Galerkin method for anisotropic nonhomogeneous diffusion, vol.304, pp.118-139, 2016.

R. Herbin and F. Hubert, Benchmark on discretization schemes for anisotropic diffusion problems on general grids, Finite Volumes for Complex Applications V, pp.659-692, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00429843

N. Ahmed and D. K. Sunada, Nonlinear ow in porous media, journal of the Hydraulics Division, vol.95, issue.6, p.18471858, 1969.

R. Alford, K. Kelly, and D. M. Boore, Accuracy of nite-dierence modeling of the acoustic wave equation, Geophysics, vol.39, issue.6, p.834842, 1974.

A. Alipour, S. Wulngho, H. R. Bayat, S. Reese, and B. Svendsen, The concept of control points in hybrid discontinuous galerkin methodsapplication to geometrically nonlinear crystal plasticity, International Journal for Numerical Methods in Engineering, vol.114, issue.5, p.557579, 2018.

D. Arnold, F. Brezzi, B. Cockburn, and L. Marini, Unied Analysis of Discontinuous Galerkin Methods for Elliptic Problems, SIAM Journal on Numerical Analysis, vol.39, issue.5, pp.1749-1779, 2002.

D. N. Arnold, An interior penalty nite element method with discontinuous elements, SIAM journal on numerical analysis, vol.19, issue.4, p.742760, 1982.

D. N. Arnold, D. P. Bo, and R. S. Falk, Quadrilateral h (div) nite elements, SIAM Journal on Numerical Analysis, vol.42, issue.6, p.24292451, 2005.

I. Babu²ka, The nite element method with lagrangian multipliers, Numerische Mathematik, vol.20, issue.3, p.179192, 1973.

G. A. Baker, Finite element methods for elliptic equations using nonconforming elements, Mathematics of Computation, vol.31, issue.137, p.4559, 1977.

F. Bassi and S. Rebay, A high-order accurate discontinuous nite element method for the numerical solution of the compressible navierstokes equations, Journal of computational physics, vol.131, issue.2, p.267279, 1997.

F. Bassi, S. Rebay, G. Mariotti, S. Pedinotti, and M. Savini, A high-order accurate discontinuous nite element method for inviscid and viscous turbomachinery ows, 93 Proceedings of the 2nd European Conference on Turbomachinery Fluid Dynamics and Thermodynamics, p.99109, 1997.

C. E. Baumann and J. T. Oden, A discontinuous hp nite element method for convectiondiusion problems, Computer Methods in Applied Mechanics and Engineering, vol.175, issue.3-4, p.311341, 1999.

J. Bear, Dynamics of uids in porous media, 1972.

J. Bear, Seawater intrusion into coastal aquifers, 2006.

T. L. Bergman, F. P. Incropera, A. S. Lavine, and D. P. Dewitt, Introduction to heat transfer, 2011.

F. Brezzi and D. Arnold, Mixed and nonconforming nite element methods :implementation,postprocessing and error estimates. Modélisation mathématique et analyse numérique, vol.19, p.732, 1985.

F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, 1991.

F. Brezzi, G. Manzini, D. Marini, P. Pietra, and A. Russo, Discontinuous galerkin approximations for elliptic problems, Numerical Methods for Partial Dierential Equations, vol.16, issue.4, p.365378, 2000.

. Brgm, Hydrogéologie de la réunion, informations générales, 2006.

P. Castillo, B. Cockburn, I. Perugia, and D. Schötzau, An a priori error analysis of the local discontinuous galerkin method for elliptic problems, SIAM Journal on Numerical Analysis, vol.38, issue.5, p.16761706, 2000.

J. R. Cavalcanti, M. Dumbser, D. Da-motta-marques, and C. R. Junior, A conservative nite volume scheme with time-accurate local time stepping for scalar transport on unstructured grids, Advances in water resources, vol.86, p.217230, 2015.

B. Cockburn, D. A. Di-pietro, and A. Ern, Bridging the hybrid high-order and hybridizable discontinuous galerkin methods, ESAIM : Mathematical Modelling and Numerical Analysis, vol.50, issue.3, p.635650, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01115318

B. Cockburn, B. Dong, and J. Guzmán, A superconvergent ldg-hybridizable galerkin method for second-order elliptic problems, Mathematics of Computation, vol.77, issue.264, pp.1887-1916, 2008.

B. Cockburn, J. Gopalakrishnan, and R. Lazarov, Unied hybridization of discontinuous galerkin, mixed, and continuous galerkin methods for second order elliptic problems

, SIAM Journal on Numerical Analysis, vol.47, issue.2, p.13191365, 2009.

B. Cockburn, W. Qiu, and K. Shi, Conditions for superconvergence of hdg methods for second-order elliptic problems, Mathematics of Computation, vol.81, issue.279, p.13271353, 2012.

B. Cockburn and C. Shu, The local discontinuous galerkin method for timedependent convection-diusion systems, SIAM Journal on Numerical Analysis, vol.35, issue.6, p.24402463, 1998.

C. Cockburn, B. Dong, and J. Guzmán, A superconvergent ldg-hybridizable galerkin method for second-order elliptic problems. Mathematics of Computation, 2008.

H. Darcy, Les Fontaines publiques de la ville de Dijon, 1856.

J. Donea, S. Giuliani, and J. Halleux, An arbitrary lagrangian-eulerian nite element method for transient dynamic uid-structure interactions, Computer methods in applied mechanics and engineering, vol.33, issue.1-3, p.689723, 1982.

J. Douglas and T. Dupont, Interior penalty procedures for elliptic and parabolic galerkin methods, Computing methods in applied sciences, p.207216, 1976.

H. Egger and J. Schoëberl, A mixed-hybrid-discontinuous galerkin nite element method for convection-diusion problems, IMA J. Numer. Anal, 2009.

A. Ern, Aide-mémoire des éléments nis. Dunod, 2005.

A. Ern and J. Guermond, Eléments nis : théorie, applications, mise en oeuvre, vol.36, 2002.

R. Eymard, T. Gallouët, and R. Herbin, Finite volume methods
URL : https://hal.archives-ouvertes.fr/hal-02100732

P. Fernandez, N. C. Nguyen, and J. Peraire, The hybridized discontinuous galerkin method for implicit large-eddy simulation of transitional turbulent ows, Journal of Computational Physics, vol.336, p.308329, 2017.

V. Fontaine, Quelques méthodes numériques robustes pour les modèles de transfert diffusif en milieu poreux, Anis Mécanique des uides, 2008.

R. A. Freeze and . Grounxdwater, , 1979.

N. Frissant, C. René-corail, J. Bonnier, and Y. De-la-torre, Le phénomène d'intrusion saline à la réunion : état des connaissances et synthèse des données disponibles, p.64, 2005.

C. G. and T. Cl, Régimes d'écoulement en milieu poreux et limite de la loi de darcy, La Houille Blanche, vol.2, p.141148, 1967.

J. H. Cooper, A hypothesis concerning the dynamic balance of fresh water and salt water in a coastal aquifer, JOURNAL OF GEOPHYSICAL RESEARCH, vol.64, issue.4, p.1959

H. Hoteit, Simulation d'écoulements et de transports de polluants en milieu poreux : application à la modélisation de la sûreté des dépôts de déchets radioactifs, Rennes, vol.1, 2002.

T. J. Hughes, W. K. Liu, and T. K. Zimmermann, Lagrangian-eulerian nite element formulation for incompressible viscous ows, Computer methods in applied mechanics and engineering, vol.29, issue.3, p.329349, 1981.

M. G. Larson and A. Målqvist, A posteriori error estimates for mixed nite element approximations of elliptic problems, Numerische Mathematik, vol.108, issue.3, p.487500, 2008.

E. Ledoux, Modèles mathématiques en hydrogéologie. Cours-Centre d'Informatique Géologique, 2003.

C. Lehrenfeld, Hybrid discontinuous galerkin methods for solving incompressible ow problems, 2010.

C. Lehrenfeld and J. Schöberl, High order exactly divergence-free hybrid discontinuous galerkin methods for unsteady incompressible ows, Computer Methods in Applied Mechanics and Engineering, vol.307, p.339361, 2016.

R. Lemaitre and P. Adler, Fractal porous media iv : three-dimensional stokes ow through random media and regular fractals, Transport in Porous Media, vol.5, issue.4, p.325340, 1990.

L. Li, S. Lanteri, N. A. Mortensen, and M. Wubs, A hybridizable discontinuous galerkin method for solving nonlocal optical response models, Computer Physics Communications, vol.219, p.99107, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01402634

G. D. Marsily, Hydrogà c ologie quantitative, 1981.

M. M. Meerschaert and C. Tadjeran, Finite dierence approximations for fractional advectiondispersion ow equations, Journal of Computational and Applied Mathematics, vol.172, issue.1, p.6577, 2004.

J. Moortgat, M. A. Amooie, and M. R. Soltanian, Implicit nite volume and discontinuous galerkin methods for multicomponent ow in unstructured 3d fractured porous media, Advances in water resources, vol.96, p.389404, 2016.

M. Mu and J. Xu, A two-grid method of a mixed stokesdarcy model for coupling uid ow with porous media ow, SIAM Journal on Numerical Analysis, vol.45, issue.5, p.18011813, 2007.

J. C. Nedelec, A new family of mixed nite elements in r3, Numerische Mathematik, vol.50, issue.1, p.5781, 1986.

N. C. Nguyen, J. Peraire, and B. Cockburn, An implicit high-order hybridizable discontinuous Galerkin method for linear convectiondiusion equations, Journal of Computational Physics, vol.228, issue.9, p.32323254, 2009.

N. C. Nguyen, J. Peraire, and B. Cockburn, A hybridizable discontinuous galerkin method for stokes ow, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.912, p.582597, 2010.

N. C. Nguyen, J. Peraire, and B. Cockburn, An implicit high-order hybridizable discontinuous galerkin method for the incompressible navier-stokes equations, J. Comput. Phys, vol.230, issue.4, p.11471170, 2011.

I. Oikawa, A hybridized discontinuous galerkin method with reduced stabilization, Journal of Scientic Computing, vol.65, issue.1, p.327340, 2015.

T. J. Povich, C. N. Dawson, M. W. Farthing, and C. E. Kees, Finite element methods for variable density ow and solute transport, Computational Geosciences, vol.17, issue.3, p.529549, 2013.

G. Puaux, Simulation numérique des écoulements aux échelles microscopique et mésoscopique dans le procédé RTM, 2011.

P. A. Raviart and J. M. Thomas, A mixed nite element method for 2-nd order elliptic problems, p.292315, 1977.

W. Reed and T. Hill, Triangular mesh method for the neutron transport equation, Proceedings of the American Nuclear Society, 1973.

J. Rubin, Transport of reacting solutes in porous media : Relation between mathematical nature of problem formulation and chemical nature of reactions, Water resources research, vol.19, issue.5, p.12311252, 1983.

T. H. Sandve, I. Berre, and J. M. Nordbotten, An ecient multi-point ux approximation method for discrete fracturematrix simulations, Journal of Computational Physics, vol.231, issue.9, p.37843800, 2012.

A. D. Santos, C. Faria, and A. Loula, A stabilized hybrid discontinuous galerkin method for nearly incompressible linear elasticity problem, Tendencias em Matematica Aplicada e Computacional, vol.18, issue.1, p.467477, 2017.

J. Shen, Mixed nite element methods on distorted rectangular grids, p.9413, 1994.

M. Stanglmeier, N. Nguyen, J. Peraire, and B. Cockburn, An explicit hybridizable discontinuous galerkin method for the acoustic wave equation, Computer Methods in Applied Mechanics and Engineering, vol.300, p.748769, 2016.

C. Steefel, C. Appelo, B. Arora, D. Jacques, T. Kalbacher et al., Reactive transport codes for subsurface environmental simulation, Computational Geosciences, vol.19, issue.3, p.445478, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01223868

J. Taine and J. Petit, Transferts thermiques. Sciences Sup. Paris, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00262470

A. Tandia, E. Diop, and C. Gaye, Pollution par les nitrates des nappes phréatiques sous environnement semi-urbain non assaini : Example de la nappe de yeumbeul, sénégal, Journal of African earth sciences, vol.29, issue.4, p.809822, 1999.

A. F. Tompson and L. W. Gelhar, Numerical simulation of solute transport in three-dimensional, randomly heterogeneous porous media, Water Resources Research, vol.26, issue.10, p.25412562, 1990.

F. Vidal-codina, N. C. Nguyen, S. Oh, and J. Peraire, A hybridizable discontinuous galerkin method for computing nonlocal electromagnetic eects in three-dimensional metallic nanostructures, Journal of Computational Physics, vol.355, p.548565, 2018.

J. Virieux, Sh-wave propagation in heterogeneous media : Velocity-stress nite-dierence method, Geophysics, vol.49, issue.11, p.19331942, 1984.

Q. Wang, Y. Ren, and W. Li, Compact high order nite volume method on unstructured grids ii : Extension to two-dimensional euler equations, Journal of Computational Physics, vol.314, p.883908, 2016.

A. D. Werner and C. T. Simmons, Impact of sea-level rise on sea water intrusion in coastal aquifers, Groundwater, vol.47, issue.2, 2009.

M. F. Wheeler, An elliptic collocation-nite element method with interior penalties, SIAM Journal on Numerical Analysis, vol.15, issue.1, p.152161, 1978.

M. Wol, B. Flemisch, R. Helmig, and I. Aavatsmark, Treatment of tensorial relative permeabilities with multipoint ux approximation, International Journal of Numerical

). .. , Porosité de quelques matériaux

. .. , Relation entre les modèles d'écoulement et de transport, p.16

, Diérentes méthodes d'éléments nis mixtes discontinus de Galerkin pour le problème de diusion

. .. Diérentes-méthodes-hybrides,

, Historique de convergence du problème de diusion isotrope en milieu homogène pour les méthodes H-RT et HdG

, Historique de convergence du problème de diusion isotrope en milieu homogène pour la méthode H-RT m

, Historique de convergence du problème de diusion-convection isotrope en milieu homogène pour la méthode H-RT m

A. , Coecients des fonctions d'interpolation µ i (x) pour p ? 2, p.88

, Coecients des fonctions d'interpolation q i (x, y) pour p ? 2, p.89

, Coecients des fonctions d'interpolation w i (x, y) pour p ? 2 (DDL= Degrés De Liberté)

. .. Schéma,

, Micro-structure d'un matériau obtenue par micro-tomographie à rayon X

V. ;. Porosité, svg)

, Schéma représentant un écoulement en milieu poreux du point de vue microscopique

.. .. Élément-de-référence-triangulaire,

H. and H. , Évaluation du temps de calcul pour les méthodes HdG

?. Domaine and . .. De-diusion-convection, 61 à l'exception de l'axe vertical en x = 0.667 où h ?1 = 230, p.61

. .. , , p.62