J. Aghili, S. Boyaval, and D. A. Di-pietro, Abstract, Computational Methods in Applied Mathematics, vol.15, issue.2, pp.111-134, 2015.
DOI : 10.1515/cmam-2015-0004

G. Allaire, Analyse numérique et optimisation Palaiseau: Les Éditions de l'École Polytechnique, 2009.

V. Anaya, G. N. Gatica, D. Mora, and R. Ruiz-baier, An augmented velocity-vorticity-pressure formulation for the Brinkman equations, International Journal for Numerical Methods in Fluids, vol.4, issue.1, pp.109-137, 2015.
DOI : 10.1051/m2an:2006036

V. Anaya, D. Mora, R. Oyarzúa, and R. Ruiz-baier, A priori and a posteriori error analysis of a mixed scheme for the Brinkman problem, Numerische Mathematik, vol.52, issue.1, pp.781-817, 2016.
DOI : 10.1137/120884109

R. Araya, C. Harder, A. H. Poza, and F. Valentin, Multiscale hybrid-mixed method for the Stokes and Brinkman equations???The method, Computer Methods in Applied Mechanics and Engineering, vol.324, pp.29-53, 2017.
DOI : 10.1016/j.cma.2017.05.027
URL : https://hal.archives-ouvertes.fr/hal-01347517

D. N. Arnold, F. Brezzi, and M. Fortin, A stable finite element for the stokes equations, Calcolo, vol.21, issue.4, pp.337-344, 1984.
DOI : 10.1007/BF02576171

L. Beirão-da-veiga, C. Lovadina, and G. Vacca, Divergence free virtual elements for the stokes problem on polygonal meshes, ESAIM: Mathematical Modelling and Numerical Analysis, vol.169, issue.2, pp.509-535, 2017.
DOI : 10.1007/978-0-387-75934-0

D. Boffi, F. Brezzi, and M. Fortin, Mixed finite element methods and applications, 2013.
DOI : 10.1007/978-3-642-36519-5

M. Botti, D. A. Di-pietro, and P. Sochala, A Hybrid High-Order Method for Nonlinear Elasticity, SIAM Journal on Numerical Analysis, vol.55, issue.6, pp.2687-2717, 2017.
DOI : 10.1137/16M1105943
URL : https://hal.archives-ouvertes.fr/hal-01539510

F. Boyer and P. Fabrie, Mathematical tools for the study of the incompressible Navier-Stokes equations and related models Applied Mathematical Sciences, p.525, 2013.

M. Braack and F. Schieweck, Equal-order finite elements with local projection stabilization for the Darcy???Brinkman equations, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.9-12, pp.9-12, 2011.
DOI : 10.1016/j.cma.2010.06.034

S. C. Brenner, Korn's inequalities for piecewise $H^1$ vector fields, Math. Comp. 73, pp.1067-1087, 2004.
DOI : 10.1090/S0025-5718-03-01579-5
URL : http://www.ams.org/mcom/2004-73-247/S0025-5718-03-01579-5/S0025-5718-03-01579-5.pdf

E. Burman and P. Hansbo, A unified stabilized method for Stokes??? and Darcy's equations, Journal of Computational and Applied Mathematics, vol.198, issue.1, pp.35-51, 2007.
DOI : 10.1016/j.cam.2005.11.022

E. Cáceres, G. N. Gatica, and F. A. Sequeira, A mixed virtual element method for the Brinkman problem, Mathematical Models and Methods in Applied Sciences, vol.27, issue.04, pp.707-743, 2017.
DOI : 10.1137/120884109

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, pp.635-650, 2016.
DOI : 10.1007/978-3-642-22980-0
URL : https://hal.archives-ouvertes.fr/hal-01115318

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.3-33, 1973.
DOI : 10.1016/B978-0-12-068650-6.50020-4

D. A. Di-pietro and J. Droniou, Ws,p-approximation properties of elliptic projectors on polynomial spaces, with application to the error analysis of a Hybrid High-Order discretisation of Leray???Lions problems, Mathematical Models and Methods in Applied Sciences, vol.9, issue.05, pp.879-908, 1142.
DOI : 10.1007/PL00005470

D. A. Di-pietro and J. Droniou, A Hybrid High-Order method for Leray???Lions elliptic equations on general meshes, Mathematics of Computation, vol.86, issue.307, 2017.
DOI : 10.1090/mcom/3180
URL : https://hal.archives-ouvertes.fr/hal-01183484

D. A. Di-pietro, J. Droniou, and A. Ern, A Discontinuous-Skeletal Method for Advection-Diffusion-Reaction on General Meshes, SIAM Journal on Numerical Analysis, vol.53, issue.5, pp.2135-2157, 1137.
DOI : 10.1137/140993971
URL : https://hal.archives-ouvertes.fr/hal-01079342

D. A. Di-pietro and A. Ern, A hybrid high-order locking-free method for linear elasticity on general meshes, Computer Methods in Applied Mechanics and Engineering, vol.283, pp.1-21, 2015.
DOI : 10.1016/j.cma.2014.09.009
URL : https://hal.archives-ouvertes.fr/hal-00979435

D. A. Di-pietro and A. Ern, Arbitrary-order mixed methods for heterogeneous anisotropic diffusion on general meshes, IMA Journal of Numerical Analysis, vol.8, issue.36, pp.40-63, 2017.
DOI : 10.1090/S0025-5718-2014-02852-4
URL : https://hal.archives-ouvertes.fr/hal-00918482

D. A. Di-pietro and A. Ern, Mathematical aspects of discontinuous Galerkin methods, Mathématiques & Applications (Berlin) [Mathematics & Applications, p.384, 2012.
DOI : 10.1007/978-3-642-22980-0

D. A. Di-pietro, A. Ern, and S. Lemaire, Abstract, Computational Methods in Applied Mathematics, vol.14, issue.4, pp.461-472, 2014.
DOI : 10.1515/cmam-2014-0018
URL : https://hal.archives-ouvertes.fr/hal-00318390

D. A. Di-pietro, A. Ern, A. Linke, and F. Schieweck, A discontinuous skeletal method for the viscosity-dependent Stokes problem, Computer Methods in Applied Mechanics and Engineering, vol.306, pp.175-195, 2016.
DOI : 10.1016/j.cma.2016.03.033
URL : https://hal.archives-ouvertes.fr/hal-01244387

D. A. Di-pietro and R. Specogna, An a posteriori-driven adaptive Mixed High-Order method with application to electrostatics, Journal of Computational Physics, vol.326, pp.35-55, 2016.
DOI : 10.1016/j.jcp.2016.08.041
URL : https://hal.archives-ouvertes.fr/hal-01310313

D. A. Di-pietro and R. Tittarelli, Lectures from the fall 2016 thematic quarter at Institut Henri Poincaré Chap. An introduction to Hybrid High-Order methods, 2018.

J. Droniou, R. Eymard, T. Gallouët, C. Guichard, and R. Herbin, The gradient discretisation method: A framework for the discretisation and numerical analysis of linear and nonlinear elliptic and parabolic problems, 2017.

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, 2004.

J. A. Evans and T. J. Hughes, Isogeometric divergence-conforming B-splines for the Darcy-Stokes-Brinkman equations, In: Math. Models Methods Appl. Sci, vol.234, pp.671-741, 1142.
DOI : 10.21236/ada555390
URL : http://www.dtic.mil/dtic/tr/fulltext/u2/a555390.pdf

G. N. Gatica, A simple introduction to the mixed finite element method, SpringerBriefs in Mathematics. Theory and applications, vol.978, pp.132-978, 2014.
DOI : 10.1007/978-3-319-03695-3

V. Girault and P. Raviart, Finite element methods for Navier-Stokes equations, Series in Computational Mathematics. Theory and algorithms, pp.374-377, 1986.
DOI : 10.1007/978-3-642-61623-5

M. Juntunen and R. Stenberg, Analysis of finite element methods for the Brinkman problem, Calcolo, vol.18, issue.1???3, pp.129-147, 2010.
DOI : 10.1016/j.crma.2009.03.010

J. Könnö and R. Stenberg, H(div)-conforming finite elements for the Brinkman problem, Math. Models Methods Appl. Sci, vol.2111, pp.2227-2248, 2011.

K. A. Mardal, X. Tai, and R. Winther, A Robust Finite Element Method for Darcy--Stokes Flow, SIAM Journal on Numerical Analysis, vol.40, issue.5, pp.1605-1631, 1137.
DOI : 10.1137/S0036142901383910

L. Mu, J. Wang, and X. Ye, A stable numerical algorithm for the Brinkman equations by weak Galerkin finite element methods, Journal of Computational Physics, vol.273, pp.327-342, 2014.
DOI : 10.1016/j.jcp.2014.04.017

J. Nédélec, Mixed finite elements in ?3, Numerische Mathematik, vol.12, issue.3, pp.315-341, 1980.
DOI : 10.1007/BF01396415

J. R. Philips, Issues in flow and transport in heterogeneous porous media, Transport in Porous Media, vol.1, issue.4, pp.319-338, 1986.
DOI : 10.1007/BF00208041

P. Raviart and J. M. Thomas, A mixed finite element method for 2-nd order elliptic problems, Proc. Conf., Consiglio Naz. delle Ricerche, pp.292-315, 1975.
DOI : 10.1007/BF01436186

C. Taylor and P. Hood, A numerical solution of the Navier-Stokes equations using the finite element technique, Computers & Fluids, vol.1, issue.1, pp.73-100, 1973.
DOI : 10.1016/0045-7930(73)90027-3

A. Tiero, On Korn's Inequality in the Second Case, Journal of Elasticity, vol.543, pp.187-1911007549427722, 1999.

G. Vacca, An H1-conforming virtual element for Darcy and Brinkman equations, Mathematical Models and Methods in Applied Sciences, vol.26, issue.01, pp.159-194, 2018.
DOI : 10.1142/S021820251650041X
URL : http://arxiv.org/pdf/1701.07680