G. Allaire, Shape optimization by the homogenization method, Applied Mathematical Sciences, vol.146, 2002.
DOI : 10.1007/s002110050253

M. Avellaneda and F. Lin, Compactness methods in the theory of homogenization. II. Equations in nondivergence form, Comm. Pure Appl. Math, vol.42, issue.2, pp.139-172, 1989.

M. Avellaneda and F. Lin, L p bounds on singular integrals in homogenization, Comm. Pure Appl. Math, vol.44, issue.8-9, pp.897-910, 1991.
DOI : 10.1002/cpa.3160440805

I. Babu?ka, Computation of derivatives in the finite element method, Comment. Math. Univ. Carolinae, vol.11, pp.545-558, 1970.

A. Bensoussan, L. Boccardo, and F. Murat, Homogenization of elliptic equations with principal part not in divergence form and Hamiltonian with quadratic growth, Comm. Pure Appl. Math, vol.39, issue.6, pp.769-805, 1986.

A. Bensoussan, J. Lions, and G. Papanicolaou, Asymptotic analysis for periodic structures, 2011.
DOI : 10.1090/chel/374

V. I. Bogachev, N. V. Krylov, and M. Röckner, On regularity of transition probabilities and invariant measures of singular diffusions under minimal conditions, Comm. Partial Differential Equations, vol.26, pp.2037-2080, 2001.

V. I. Bogachev and S. V. Shaposhnikov, Integrability and continuity of solutions to double divergence form equations, Ann. Mat. Pura Appl, vol.196, issue.4, pp.1609-1635, 2017.
DOI : 10.1007/s10231-016-0631-2

D. Cioranescu and P. Donato, An introduction to homogenization, Oxford Lecture Series in Mathematics and its Applications, vol.17, 1999.

Y. Efendiev and T. Y. Hou, Multiscale finite element methods, volume 4 of Surveys and Tutorials in the Applied Mathematical Sciences, Theory and applications, 2009.

B. D. Froese and A. M. Oberman, Numerical averaging of non-divergence structure elliptic operators, Commun. Math. Sci, vol.7, issue.4, pp.785-804, 2009.
DOI : 10.4310/cms.2009.v7.n4.a1
URL : http://www.intlpress.com/site/pub/files/_fulltext/journals/cms/2009/0007/0004/CMS-2009-0007-0004-a001.pdf

D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, Classics in Mathematics, 2001.
DOI : 10.1007/978-3-642-96379-7

P. Grisvard, Elliptic problems in nonsmooth domains, Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), vol.69, 2011.
DOI : 10.1137/1.9781611972030

F. Hecht, New development in freefem++, J. Numer. Math, vol.20, issue.3-4, pp.251-265, 2012.
DOI : 10.1515/jnum-2012-0013
URL : https://hal.archives-ouvertes.fr/hal-01476313

T. Hell and A. Ostermann, Compatibility conditions for Dirichlet and Neumann problems of Poisson's equation on a rectangle, J. Math. Anal. Appl, vol.420, issue.2, pp.1005-1023, 2014.

T. Hell, A. Ostermann, and M. Sandbichler, Modification of dimension-splitting methodsovercoming the order reduction due to corner singularities, IMA J. Numer. Anal, vol.35, issue.3, pp.1078-1091, 2015.

T. Kinoshita, Y. Watanabe, N. Yamamoto, and M. T. Nakao, Some remarks on a priori estimates of highly regular solutions for the Poisson equation in polygonal domains, Jpn. J. Ind. Appl. Math, vol.33, issue.3, pp.629-636, 2016.

A. H. Schatz, An observation concerning Ritz-Galerkin methods with indefinite bilinear forms, Math. Comp, vol.28, pp.959-962, 1974.
DOI : 10.1090/s0025-5718-1974-0373326-0
URL : https://www.ams.org/mcom/1974-28-128/S0025-5718-1974-0373326-0/S0025-5718-1974-0373326-0.pdf

I. Smears and E. Süli, Discontinuous Galerkin finite element approximation of nondivergence form elliptic equations with Cordès coefficients, SIAM J. Numer. Anal, vol.51, issue.4, pp.2088-2106, 2013.
DOI : 10.1137/120899613
URL : http://discovery.ucl.ac.uk/1572511/1/SIAM%20J.%20Numer.%20Anal.%202013%20Smears.pdf

L. Tartar, The general theory of homogenization, Lecture Notes of the Unione Matematica Italiana, vol.7, 2009.

, Capdeboscq: yves.capdeboscq@sorbonne-universite.fr ( ?) University of Oxford, Mathematical Institute, Woodstock Road, Oxford OX2 6GG, UK. Email address, T. Sprekeler: timo.sprekeler@maths.ox.ac.uk ( ?) University of