R. [. Allaire and . Brizzi, A Multiscale Finite Element Method for Numerical Homogenization, Multiscale Modeling & Simulation, vol.4, issue.3, pp.790-812, 2006.
DOI : 10.1137/040611239

H. [. Assyr and . Ernst, Discontinuous galerkin finite element heterogeneous multiscale method for advection?diffusion problems with multiple scales, Numer. Math, vol.126, issue.4, pp.589-633, 2014.

. W. Bhk, T. Bangerth, G. Heister, and . Kanschat, deal.II Differential Equations Analysis Library, Technical Reference

F. [. Bris, F. Legoll, and . Madiot, A numerical comparison of some multiscale finite element approaches for convection-dominated problems in heterogeneous media. arXiv preprint, 2015.

M. [. Chen, T. Y. Cui, X. Savchuk, and . Yu, The Multiscale Finite Element Method with Nonconforming Elements for Elliptic Homogenization Problems, Multiscale Modeling & Simulation, vol.7, issue.2, pp.517-538, 2008.
DOI : 10.1137/070691917

T. [. Efendiev and . Hou, Multiscale finite element methods: theory and applications, 2009.

T. [. Efendiev, X. Hou, and . 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

]. D. Elf15 and . Elfverson, A discontinuous galerkin multiscale method for convection-diffusion problems, 2015.

A. [. Ern, M. Nicaise, and . Vohlarik, An accurate h(div) flux reconstruction for discontinuous galerkin approximations of elliptic problems, 2007.

C. Lawrence and . Evans, Partial differential equations, 2010.

S. Fei and D. Weibing, Multiscale discontinuous petrov?galerkin method for the multiscale elliptic problems. arXiv preprint, 2017.

A. Gloriaho10, ]. P. Henning, and M. Ohlberger, REDUCTION OF THE RESONANCE ERROR ??? PART 1: APPROXIMATION OF HOMOGENIZED COEFFICIENTS, Mathematical Models and Methods in Applied Sciences, vol.25, issue.08, pp.1601-1630711, 2010.
DOI : 10.1016/j.jcp.2006.07.034

. Y. Th, X. H. Hou, and . Wu, A multiscale finite element method for elliptic problems in composite materials and porous media, J. Comput. Phys, vol.134, pp.169-189, 1997.

P. Jenny, H. Lee, and . Tchelepi, Multi-scale finite-volume method for elliptic problems in subsurface flow simulation, Journal of Computational Physics, vol.187, issue.1, pp.47-67, 2003.
DOI : 10.1016/S0021-9991(03)00075-5

[. Jenny, H. Lee, and . Tchelepi, Adaptive Multiscale Finite-Volume Method for Multiphase Flow and Transport in Porous Media, Multiscale Modeling & Simulation, vol.3, issue.1, pp.50-64, 2005.
DOI : 10.1137/030600795

A. Konaté, Méthode multi-´ echelle pour la simulation d'´ ecoulements miscibles en milieux poreux, 2017.

]. F. Mad16 and . Madiot, Multiscale finite element methods for advection diffusion problems, 2016.

F. Ouaki, G. Allaire, S. Desroziers, and G. Enchéry, A priori error estimate of a multiscale finite element method for transport modeling, SeMA Journal, vol.10, issue.4, pp.1-37, 2015.
DOI : 10.1137/0710062

URL : https://hal.archives-ouvertes.fr/hal-01071637

]. F. Oua13 and . Ouaki, Etude de schémas multi-´ echelles pour la simulation de réservoir, Thèse de doctorat de l'Ecole Polytechnique, 2013.