]. A. Bibliographie1, J. Agouzal, and . Thomas, An extension theorem for equilibrium finite elements spaces, Japan J. of Indust. Appl. Math, vol.13, pp.257-266, 1996.

M. Ainsworth, A Posteriori Error Estimation for Discontinuous Galerkin Finite Element Approximation, SIAM Journal on Numerical Analysis, vol.45, issue.4, 2006.
DOI : 10.1137/060665993

M. Ainsworth and J. Oden, A posteriori error estimation in finite element analysis, Computer Methods in Applied Mechanics and Engineering, vol.142, issue.1-2, 2000.
DOI : 10.1016/S0045-7825(96)01107-3

D. G. 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, 2001.
DOI : 10.1137/S0036142901384162

F. Assous, P. Ciarlet, and E. Sonnendrücker, Resolution of the Maxwell equations in a domain with reentrant corners, ESAIM: Mathematical Modelling and Numerical Analysis, vol.32, issue.3, pp.359-389, 1998.
DOI : 10.1051/m2an/1998320303591

URL : https://hal.archives-ouvertes.fr/hal-01010426

I. Babu?ka and T. Strouboulis, The finite element methods and its reliability, 2001.

R. Bank and R. Smith, A Posteriori Error Estimates Based on Hierarchical Bases, SIAM Journal on Numerical Analysis, vol.30, issue.4, pp.921-935, 1993.
DOI : 10.1137/0730048

R. Beck, P. Deuflhard, R. Hiptmair, R. Hoppe, and B. Wohlmuth, Adaptive multilevel methods for edge element discretizations of Maxwell's equations, Surveys of Math. in Industry, vol.8, pp.271-312, 1999.

R. Beck, R. Hiptmair, R. Hoppe, and B. Wohlmuth, Residual based a posteriori error estimators for eddy current computation, ESAIM: Mathematical Modelling and Numerical Analysis, vol.34, issue.1, pp.159-182, 2000.
DOI : 10.1051/m2an:2000136

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.27.7561

R. Becker, P. Hansbo, and M. G. Larson, Energy norm a posteriori error estimation for discontinuous Galerkin methods, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.5-6, pp.723-733, 2003.
DOI : 10.1016/S0045-7825(02)00593-5

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.3977

C. Bernardi and R. Verfürth, Adaptive finite element methods for elliptic equations with non-smooth coefficients, Numerische Mathematik, vol.85, issue.4, pp.579-608, 2000.
DOI : 10.1007/PL00005393

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.407

A. Bossavit, Computational electromagnetism. Variational formulations, complementarity , edge elements, 1998.

D. Braess and J. Schöberl, Equilibrated residual error estimator for Maxwell's equations, Austrian Acad. Sciences, 2006.

S. C. Brenner and L. R. Scott, The mathematical theory of finite element methods, 1994.

F. Brezzi and M. Fortin, Mixed and hybrid finite element methods, 1991.
DOI : 10.1007/978-1-4612-3172-1

M. F. Brivì-ere and . Wheeler, A posteriori error estimates for a discontinuous galerkin method applied to elliptic problems, Comput. Math. Appl, vol.46, issue.1, pp.141-163, 2003.

P. Ciarlet, The finite element method for elliptic problems, 1978.

P. Clément, Approximation by finite element functions using local regularization, Revue fran??aise d'automatique, informatique, recherche op??rationnelle. Analyse num??rique, vol.9, issue.R2, pp.77-84, 1975.
DOI : 10.1051/m2an/197509R200771

S. Cochez-dhondt and S. Nicaise, Robust a posteriori error estimation for the Maxwell equations, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.25-28, pp.2583-2595, 2007.
DOI : 10.1016/j.cma.2006.11.025

B. Cockburn, G. E. Karniadakis, and C. Shu, The Development of Discontinuous Galerkin Methods, Lect. Notes Comput. Sci. Eng, vol.11, 2000.
DOI : 10.1007/978-3-642-59721-3_1

M. Costabel and M. Dauge, Singularities of Electromagnetic Fields??in Polyhedral Domains, Archive for Rational Mechanics and Analysis, vol.151, issue.3, pp.221-276, 2000.
DOI : 10.1007/s002050050197

M. Costabel, M. Dauge, and S. Nicaise, Singularities of Maxwell interface problems, ESAIM: Mathematical Modelling and Numerical Analysis, vol.33, issue.3, pp.627-649, 1999.
DOI : 10.1051/m2an:1999155

E. Creusé, G. Kunert, and S. Nicaise, ERROR ESTIMATION FOR THE STOKES PROBLEM: ANISOTROPIC AND ISOTROPIC DISCRETIZATIONS, Mathematical Models and Methods in Applied Sciences, vol.14, issue.09, pp.1297-1341, 2004.
DOI : 10.1142/S0218202504003635

E. Creusé and S. Nicaise, Anisotropica posteriori error estimation for the mixed discontinuous Galerkin approximation of the Stokes problem, Numerical Methods for Partial Differential Equations, vol.19, issue.2, pp.449-483, 2006.
DOI : 10.1002/num.20107

E. Dari, R. Duràn, C. Padra, and V. Vampa, A posteriori error estimators for nonconforming finite element methods, ESAIM: Mathematical Modelling and Numerical Analysis, vol.30, issue.4, pp.385-400, 1996.
DOI : 10.1051/m2an/1996300403851

V. Girault and P. Raviart, Finite elements methods for Navier-Stokes equations, Theory and Algorithms, 1986.

P. Houston, I. Perugia, and D. Schötzau, Energy norm a posteriori error estimation for mixed discontinuous Galerkin approximations of the Maxwell operator, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.2-5, pp.499-510, 2005.
DOI : 10.1016/j.cma.2004.02.025

P. Houston, I. Perugia, and D. Schötzau, An a posteriori error indicator for discontinuous Galerkin discretizations of H(curl)-elliptic partial differential equations, IMA Journal of Numerical Analysis, vol.27, issue.1, pp.122-150, 2007.
DOI : 10.1093/imanum/drl012

F. Izsák, D. Harutyunyan, J. Van, and . Vegt, A posteriori implicit error estimation for the Maxwell equations, 2005.

O. A. Karakashian and F. Pascal, A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems, SIAM Journal on Numerical Analysis, vol.41, issue.6, pp.2374-2399, 2003.
DOI : 10.1137/S0036142902405217

G. Kunert and T. Chemnitz, A posteriori error estimation for anisotropic tetrahedral and triangular finite element meshes, Logos Verlag, 1999.
DOI : 10.1093/imanum/21.2.503

URL : http://imajna.oxfordjournals.org/cgi/content/short/21/2/503

G. Kunert, An a posteriori residual error estimator for the finite element method on anisotropic tetrahedral meshes, Numerische Mathematik, vol.86, issue.3, pp.471-490, 2000.
DOI : 10.1007/s002110000170

G. Kunert, Robust a posteriori error estimation for a singularly perturbed reaction? diffusion equation on anisotropic tetrahedral meshes, Adv. Comp. Math, vol.15, pp.1-4237, 2001.

G. Kunert, A posteriori error estimation for convection dominated problems on anisotropic meshes, Mathematical Methods in the Applied Sciences, vol.86, issue.7, pp.589-617, 2003.
DOI : 10.1002/mma.368

P. Ladevèze and D. Leguillon, Error Estimate Procedure in the Finite Element Method and Applications, SIAM Journal on Numerical Analysis, vol.20, issue.3, pp.485-509, 1983.
DOI : 10.1137/0720033

R. Lazarov, S. Repin, and S. Tomar, Functional a posteriori error estimates for discontinuous Galerkin approximations of elliptic problems, Numerical Methods for Partial Differential Equations, vol.42, issue.23, 2006.
DOI : 10.1002/num.20386

S. Lohrengel and S. Nicaise, A discontinuous Galerkin method on refined meshes for the two-dimensional time-harmonic Maxwell equations in composite materials, Journal of Computational and Applied Mathematics, vol.206, issue.1, 2006.
DOI : 10.1016/j.cam.2006.05.020

R. Luce and B. Wohlmuth, A Local A Posteriori Error Estimator Based on Equilibrated Fluxes, SIAM Journal on Numerical Analysis, vol.42, issue.4, pp.1394-1414, 2004.
DOI : 10.1137/S0036142903433790

URL : https://hal.archives-ouvertes.fr/inria-00343040

P. Monk, A posteriori error indicators for Maxwell's equations, Journal of Computational and Applied Mathematics, vol.100, issue.2, pp.73-190, 1998.
DOI : 10.1016/S0377-0427(98)00187-3

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

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

P. Neittaanmaäki and S. Repin, Reliable methods for computer simulation : error control and a posteriori error estimates, of Studies in Mathematics and its applications, 2004.

S. Nicaise, Edge Elements on Anisotropic Meshes and Approximation of the Maxwell Equations, SIAM Journal on Numerical Analysis, vol.39, issue.3, pp.784-816, 2001.
DOI : 10.1137/S003614290036988X

S. Nicaise, A posteriori error estimations of some cell-centered finite volume methods, SIAM Journal on Numerical Analysis, vol.43, issue.4, pp.1481-1503, 2005.
DOI : 10.1137/S0036142903437787

S. Nicaise and E. Creusé, A posteriori error estimation for the heterogeneous Maxwell equations on isotropic and anisotropic meshes. Calcolo, pp.249-271, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00768715

S. Nicaise, K. Witowski, and B. Wohlmuth, An a posteriori error estimator for the Lame equation based on equilibrated fluxes, IMA Journal of Numerical Analysis, vol.28, issue.2, 2006.
DOI : 10.1093/imanum/drm008

J. E. Pasciak and J. Zhao, Overlapping Schwarz methods in H(curl) on polyhedral domains, Journal of Numerical Mathematics, vol.10, issue.3, pp.221-234, 2002.
DOI : 10.1515/JNMA.2002.221

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

J. Schöberl, A posteriori error estimates for Maxwell equations. Preprint, 2005.

K. Shahbazi, An explicit expression for the penalty parameter of the interior penalty method, Journal of Computational Physics, vol.205, issue.2, pp.401-407, 2005.
DOI : 10.1016/j.jcp.2004.11.017

S. Sun and M. F. Wheeler, L 2 (H 1 ) norm a posteriori error estimation for discontinuous Galerkin approximations of reactive transport problems, J. Sci. Comput, pp.22-23501, 2005.

R. Verfürth, A review of a posteriori error estimation and adaptive mesh-refinement techniques, 1996.

R. Verfürth, Robust a posteriori error estimators for singularly perturbed reactiondiffusion equations, Numer. Math, vol.78, pp.479-493, 1998.

R. Verfürth, Error estimates for some quasi-interpolation operators, ESAIM: Mathematical Modelling and Numerical Analysis, vol.33, issue.4, pp.695-713, 1999.
DOI : 10.1051/m2an:1999158