A. Abdulle, W. E. , B. Engquist, and E. Vanden-eijnden, The heterogeneous multiscale method, Acta Numerica, vol.21, pp.1-87, 2012.
DOI : 10.1017/S0962492912000025
URL : https://hal.archives-ouvertes.fr/hal-00746811

G. Allaire, Shape Optimization by the Homogenization Method, Applied Mathematical Sciences, vol.146, 2002.

G. Allaire and R. Brizzi, A Multiscale Finite Element Method for Numerical Homogenization, Multiscale Modeling & Simulation, vol.4, issue.3, pp.790-812, 2005.
DOI : 10.1137/040611239

R. Araya, C. Harder, D. Paredes, and F. Valentin, Multiscale Hybrid-Mixed Method, SIAM Journal on Numerical Analysis, vol.51, issue.6, pp.3505-3531, 2013.
DOI : 10.1137/120888223
URL : https://hal.archives-ouvertes.fr/hal-01347517

D. N. Arnold, F. Brezzi, B. Cockburn, and L. D. Marini, Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems, SIAM Journal on Numerical Analysis, vol.39, issue.5, pp.1749-1779, 2002.
DOI : 10.1137/S0036142901384162

B. Ayuso-de-dios, K. Lipnikov, and G. Manzini, The nonconforming virtual element method, M2AN), pp.879-904, 2016.
DOI : 10.1016/B978-0-12-068650-6.50030-7

F. Bassi, L. Botti, A. Colombo, D. A. Di-pietro, and P. Tesini, On the flexibility of agglomeration based physical space discontinuous Galerkin discretizations, Journal of Computational Physics, vol.231, issue.1, pp.45-65, 2012.
DOI : 10.1016/j.jcp.2011.08.018
URL : https://hal.archives-ouvertes.fr/hal-00562219

M. Bebendorf, A Note on the Poincar?? Inequality for Convex Domains, Zeitschrift f??r Analysis und ihre Anwendungen, vol.22, issue.4, pp.751-756, 2003.
DOI : 10.4171/ZAA/1170

L. Beirão-da-veiga, F. Brezzi, A. Cangiani, G. Manzini, L. D. Marini et al., BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS, M3AS), pp.199-214, 2013.
DOI : 10.1051/m2an:2008030

A. Cangiani, E. H. Georgoulis, and P. Houston, hp-version discontinuous Galerkin methods on polygonal and polyhedral meshes, Math. Models Meth. Appl. Sci, issue.M3AS10, pp.242009-2041, 2014.
DOI : 10.1007/978-3-319-67673-9

E. T. Chung, S. Fu, and Y. Yang, An enriched multiscale mortar space for high contrast flow problems, Commun. Comput. Phys, vol.23, issue.2, pp.476-499, 2018.

M. Cicuttin, D. A. Di-pietro, and A. Ern, Implementation of Discontinuous Skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming, Journal of Computational and Applied Mathematics, 2017.
DOI : 10.1016/j.cam.2017.09.017
URL : https://hal.archives-ouvertes.fr/hal-01429292

B. Cockburn, Static Condensation, Hybridization, and the Devising of the HDG Methods, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations, number 114 in Lecture Notes in Computational Science and Engineering, pp.129-177, 2016.
DOI : 10.1016/j.camwa.2014.01.019

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

B. Cockburn, J. Gopalakrishnan, and R. Lazarov, Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems, SIAM Journal on Numerical Analysis, vol.47, issue.2, pp.1319-1365, 2009.
DOI : 10.1137/070706616

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

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, Hybrid high-order methods for variable-diffusion problems on general meshes, Comptes Rendus Mathematique, vol.353, issue.1, pp.31-34, 2015.
DOI : 10.1016/j.crma.2014.10.013
URL : https://hal.archives-ouvertes.fr/hal-01023302

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, and S. Lemaire, A Review of Hybrid High-Order Methods: Formulations, Computational Aspects, Comparison with Other Methods, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations, pp.205-236, 2016.
DOI : 10.1090/S0025-5718-2014-02852-4
URL : https://hal.archives-ouvertes.fr/hal-01163569

W. E. and B. Engquist, The Heterogeneous Multiscale Methods, Comm. Math. Sci, vol.1, pp.87-132, 2003.

Y. Efendiev and T. Y. Hou, Multiscale Finite Element Methods -Theory and Applications, of Surveys and Tutorials in the Applied Mathematical Sciences, 2009.

Y. Efendiev, T. Y. Hou, and X. Wu, Convergence of a Nonconforming Multiscale Finite Element Method, SIAM Journal on Numerical Analysis, vol.37, issue.3, pp.888-910, 2000.
DOI : 10.1137/S0036142997330329

Y. Efendiev, R. Lazarov, M. Moon, and K. Shi, A spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems, Computer Methods in Applied Mechanics and Engineering, vol.292, pp.243-256, 2015.
DOI : 10.1016/j.cma.2014.09.036

Y. Efendiev, R. Lazarov, and K. Shi, A Multiscale HDG Method for Second Order Elliptic Equations. Part I. Polynomial and Homogenization-Based Multiscale Spaces, SIAM Journal on Numerical Analysis, vol.53, issue.1, pp.342-369, 2015.
DOI : 10.1137/13094089X

A. Ern and J. Guermond, Finite element quasi-interpolation and best approximation, M2AN), pp.1367-1385, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01155412

A. Ern and M. Vohralík, Stable broken H 1 and Hpdivq polynomial extensions for polynomial-degreerobust potential and flux reconstruction in three space dimensions

D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, Classics in Mathematics, 2001.

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

A. Gloria, Numerical homogenization: survey, new results, and perspectives, ESAIM: Proceedings, vol.37, pp.50-116, 2012.
DOI : 10.1051/proc/201237002
URL : https://hal.archives-ouvertes.fr/hal-00766743

P. Henning and D. Peterseim, Oversampling for the Multiscale Finite Element Method, Multiscale Modeling & Simulation, vol.11, issue.4, pp.1149-1175, 2013.
DOI : 10.1137/120900332

J. S. Hesthaven, S. Zhang, and X. Zhu, High-Order Multiscale Finite Element Method for Elliptic Problems, Multiscale Modeling & Simulation, vol.12, issue.2, pp.650-666, 2014.
DOI : 10.1137/120898024
URL : https://infoscience.epfl.ch/record/190663/files/89802.pdf

T. Y. Hou and X. Wu, A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media, Journal of Computational Physics, vol.134, issue.1, pp.169-189, 1997.
DOI : 10.1006/jcph.1997.5682

T. Y. Hou, X. Wu, and Z. Cai, Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients, Mathematics of Computation, vol.68, issue.227, pp.913-943, 1999.
DOI : 10.1090/S0025-5718-99-01077-7

T. Y. Hou, X. Wu, and Y. Zhang, Removing the Cell Resonance Error in the Multiscale Finite Element Method via a Petrov-Galerkin Formulation, Communications in Mathematical Sciences, vol.2, issue.2, pp.185-205, 2004.
DOI : 10.4310/CMS.2004.v2.n2.a3

V. V. Jikov, S. M. Kozlov, and O. A. Oleinik, Homogenization of differential operators and integral functionals, 1994.
DOI : 10.1007/978-3-642-84659-5

A. Konaté, Méthode multi-échelle pour la simulation d'écoulements miscibles en milieux poreux, p.1558994, 2017.

C. , L. Bris, F. Legoll, and A. Lozinski, MsFEM à la Crouzeix?Raviart for highly oscillatory elliptic problems, Chinese Annals of Mathematics, Series B, vol.34, issue.1, pp.113-138, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00789102

C. , L. Bris, F. Legoll, and A. Lozinski, An MsFEM-type approach for perforated domains, SIAM Multiscale Model. Simul, vol.12, issue.3, pp.1046-1077, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00841308

A. Målqvist and D. Peterseim, Localization of elliptic multiscale problems, Mathematics of Computation, vol.83, issue.290, pp.2583-2603, 2014.
DOI : 10.1090/S0025-5718-2014-02868-8

L. Mu, J. Wang, and X. Ye, A weak Galerkin generalized multiscale finite element method, Journal of Computational and Applied Mathematics, vol.305, pp.68-81, 2016.
DOI : 10.1016/j.cam.2016.03.017

D. Paredes, F. Valentin, and H. M. Versieux, On the robustness of multiscale hybrid-mixed methods, Mathematics of Computation, vol.86, issue.304, pp.525-548, 2017.
DOI : 10.1090/mcom/3108
URL : https://hal.archives-ouvertes.fr/hal-01394241

N. Sukumar and A. Tabarraei, Conforming polygonal finite elements, International Journal for Numerical Methods in Engineering, vol.40, issue.12, pp.2045-2066, 2004.
DOI : 10.1080/10867651.2002.10487551
URL : http://dilbert.engr.ucdavis.edu/~suku/nem/papers/nem_polygonfem.pdf

A. Veeser and R. Verfürth, Poincare constants for finite element stars, IMA Journal of Numerical Analysis, vol.32, issue.1, pp.30-47, 2012.
DOI : 10.1093/imanum/drr011
URL : http://www.num1.ruhr-uni-bochum.de/files/reports/Poincare.pdf

E. L. Wachspress, A Rational Finite Element Basis, Journal of Lubrication Technology, vol.98, issue.4, 1975.
DOI : 10.1115/1.3452953

J. Wang and X. Ye, A weak Galerkin finite element method for second-order elliptic problems, Journal of Computational and Applied Mathematics, vol.241, pp.103-115, 2013.
DOI : 10.1016/j.cam.2012.10.003