C. Amrouche, C. Bernardi, M. Dauge, and V. Girault, Vector potentials in three-dimensional non-smooth domains, Mathematical Methods in the Applied Sciences, vol.2, issue.9, pp.823-864, 1998.
DOI : 10.1002/mma.1670020103

D. N. Arnold, R. S. Falk, and R. Winther, Finite element exterior calculus, homological techniques, and applications, Acta Numerica, vol.15, pp.1-155, 2006.
DOI : 10.1017/S0962492906210018
URL : http://www.ifi.uio.no/~rwinther/acta.pdf

D. N. Arnold, R. S. Falk, and R. Winther, Finite element exterior calculus: from Hodge theory to numerical stability, Bulletin of the American Mathematical Society, vol.47, issue.2, pp.281-354, 2010.
DOI : 10.1090/S0273-0979-10-01278-4

M. S. Birman and M. Z. Solomyak, -Theory of the Maxwell operator in arbitrary domains, Uspekhi Mat. Nauk, pp.61-76, 1987.
DOI : 10.1070/RM1987v042n06ABEH001505

A. Blouza and H. L. Dret, An Up-to-the Boundary Version of Friedrichs's Lemma and Applications to the Linear Koiter Shell Model, SIAM Journal on Mathematical Analysis, vol.33, issue.4, pp.877-895, 2001.
DOI : 10.1137/S0036141000380012

A. Bonito, J. Guermond, and F. Luddens, Regularity of the Maxwell equations in heterogeneous media and Lipschitz domains, Journal of Mathematical Analysis and Applications, vol.408, issue.2, pp.498-512, 2013.
DOI : 10.1016/j.jmaa.2013.06.018
URL : https://hal.archives-ouvertes.fr/hal-01024489

A. Bonito, J. Guermond, and F. Luddens, An interior penalty method with C 0 finite elements for the approximation of the Maxwell equations in heterogeneous media: Convergence analysis with minimal regularity, press, pp.1402-4454, 2015.

H. Brezis, Functional analysis, Sobolev spaces and partial differential equations, 2011.
DOI : 10.1007/978-0-387-70914-7

S. Caorsi, P. Fernandes, and M. Raffetto, On the Convergence of Galerkin Finite Element Approximations of Electromagnetic Eigenproblems, SIAM Journal on Numerical Analysis, vol.38, issue.2, pp.580-607, 2000.
DOI : 10.1137/S0036142999357506

S. H. Christiansen, Stability of Hodge decompositions in finite element spaces of differential forms in arbitrary dimension, Numerische Mathematik, vol.26, issue.1, pp.87-106, 2007.
DOI : 10.1515/9781400877577

S. H. Christiansen, Upwinding in Finite Element Systems of Differential Forms, 2015.
DOI : 10.1017/CBO9781139095402.004

S. H. Christiansen and R. Winther, Smoothed projections in finite element exterior calculus, Mathematics of Computation, vol.77, issue.262, pp.813-829, 2008.
DOI : 10.1090/S0025-5718-07-02081-9

P. G. Ciarlet, The finite element method for elliptic problems, #25001)], p.520174, 1958.

A. Ern and J. Guermond, Theory and practice of finite elements, Applied Mathematical Sciences, vol.159, 2004.
DOI : 10.1007/978-1-4757-4355-5

A. Ern and J. Guermond, Finite element quasi-interpolation and best approximation, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01155412

R. S. Falk and R. Winther, Local bounded cochain projections, Mathematics of Computation, vol.83, issue.290, pp.2631-2656, 2014.
DOI : 10.1090/S0025-5718-2014-02827-5
URL : http://www.math.rutgers.edu/~falk/papers/local-cochain.pdf

K. O. Friedrichs, The identity of weak and strong extensions of differential operators, Transactions of the American Mathematical Society, vol.55, pp.132-151, 1944.
DOI : 10.1090/S0002-9947-1944-0009701-0

V. Girault and L. R. Scott, Analysis of a two-dimensional grade-two fluid model with a tangential boundary condition, Journal de Math??matiques Pures et Appliqu??es, vol.78, issue.10, pp.78981-1011, 1999.
DOI : 10.1016/S0021-7824(99)00137-3

P. Grisvard, Elliptic problems in nonsmooth domains, Monographs and Studies in Mathematics, vol.24, 1985.
DOI : 10.1137/1.9781611972030

R. Hiptmair, Finite elements in computational electromagnetism, Acta Numer, vol.11, pp.237-339, 2002.

S. Hofmann, M. Mitrea, and M. Taylor, Geometric and transformational properties of Lipschitz domains, Semmes-Kenig-Toro domains, and other classes of finite perimeter domains, Journal of Geometric Analysis, vol.59, issue.3, pp.593-647, 2007.
DOI : 10.1007/978-1-4612-1015-3

F. Kikuchi, On a discrete compactness property for the Nédélec finite elements, J. Fac. Sci. Univ. Tokyo Sect. IA Math, vol.36, issue.3, pp.479-490, 1989.

J. Leray, Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Mathematica, vol.63, issue.0, pp.193-248, 1934.
DOI : 10.1007/BF02547354
URL : http://doi.org/10.1007/bf02547354

W. Mclean, Strongly elliptic systems and boundary integral equations, 2000.

P. Monk, Finite element methods for Maxwell's equations. Numerical Mathematics and Scientific Computation, 2003.

P. Monk and L. Demkowicz, Discrete compactness and the approximation of Maxwell's equations in $\mathbb{R}^3$, Mathematics of Computation, vol.70, issue.234, pp.507-523, 2001.
DOI : 10.1090/S0025-5718-00-01229-1

J. Schöberl, Commuting quasi-interpolation operators for mixed finite elements, 2001.

J. Schöberl, A multilevel decomposition result in H(curl), Multigrid, Multilevel and Multiscale Methods, 2005.

J. Schöberl, A posteriori error estimates for Maxwell equations, Mathematics of Computation, vol.77, issue.262, pp.633-649, 2008.
DOI : 10.1090/S0025-5718-07-02030-3

S. Soboleff, Sur un théorème d'analyse fonctionnelle, Rec. Math. [Mat. Sbornik] N.S, vol.4, issue.46, pp.471-497, 1938.