M. Ainsworth, Robust a posteriori error estimation for nonconforming finite element approximation, SIAM J. Numer. Anal, vol.42, pp.2320-2341, 2005.

M. Ainsworth, A framework for obtaining guaranteed error bounds for finite element approximations, J. Comput. Appl. Math, vol.234, pp.2618-2632, 2010.

M. Alnaes, J. Blechta, J. Hake, A. Johansson, B. Kehlet et al., The FEniCS Project version 1.5. Archive of Numerical Software, vol.3, p.100, 2015.

I. Babu?ka and A. Miller, A feedback finite element method with a posteriori error estimation. I. The finite element method and some basic properties of the a posteriori error estimator, Comput. Methods Appl. Mech. Engrg, vol.61, pp.1-40, 1987.

R. Becker, D. Capatina, L. , and R. , Local flux reconstructions for standard finite element methods on triangular meshes, SIAM J. Numer. Anal, vol.54, pp.2684-2706, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01581283

C. Bernardi and R. Verfürth, Adaptive finite element methods for elliptic equations with non-smooth coefficients, Numer. Math, vol.85, pp.579-608, 2000.

J. Blechta, Dolfin-tape, DOLFIN tools for a posteriori error estimation, version "paper-norms-nonlincode-v1.0-rc3, 2016.

J. Blechta, J. Málek, and M. Vohralík, Localization of the W ?1,q norm for local a posteriori efficiency, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01332481

A. Bonnet-ben-dhia, C. Carvalho, C. , and P. , Mesh requirements for the finite element approximation of problems with sign-changing coefficients, Numer. Math, vol.138, pp.801-838, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01335153

A. Bonnet-ben-dhia, L. Chesnel, C. , and P. , T-coercivity for scalar interface problems between dielectrics and metamaterials, M2AN Math. Model. Numer. Anal, vol.46, pp.1363-1387, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00564312

A. Bonnet-bendhia, M. Dauge, R. , and K. , Analyse spectrale et singularités d'un probì eme de transmission non coercif, C. R. Acad. Sci. Paris Sér. I Math, vol.328, pp.717-720, 1999.

D. Braess, V. Pillwein, and J. Schöberl, Equilibrated residual error estimates are p-robust, Comput. Methods Appl. Mech. Engrg, vol.198, pp.1189-1197, 2009.
DOI : 10.1016/j.cma.2008.12.010
URL : http://www.risc.uni-linz.ac.at/publications/download/risc_3414/ho_equilibrated.pdf

D. Braess and J. Schöberl, Equilibrated residual error estimator for edge elements, Math. Comp, vol.77, pp.651-672, 2008.
DOI : 10.1090/s0025-5718-07-02080-7
URL : https://www.ams.org/mcom/2008-77-262/S0025-5718-07-02080-7/S0025-5718-07-02080-7.pdf

S. C. Brenner, Poincaré-Friedrichs inequalities for piecewise H 1 functions, SIAM J. Numer. Anal, vol.41, pp.306-324, 2003.
DOI : 10.1137/s0036142902401311

F. Brezzi and M. Fortin, Mixed and hybrid finite element methods, of Springer Series in Computational Mathematics, vol.15, 1991.

C. Carstensen, M. Eigel, R. H. Hoppe, L. , and C. , A review of unified a posteriori finite element error control, Numer. Math. Theory Methods Appl, vol.5, pp.509-558, 2012.
DOI : 10.4208/nmtma.2011.m1032
URL : https://opus.bibliothek.uni-augsburg.de/opus4/files/1450/mpreprint_10_013.pdf

C. Carstensen and S. A. Funken, Fully reliable localized error control in the FEM, SIAM J. Sci. Comput, vol.21, pp.1465-1484, 1999.
DOI : 10.1137/s1064827597327486

C. Carstensen, M. , and C. , Computational survey on a posteriori error estimators for nonconforming finite element methods for the Poisson problem, J. Comput. Appl. Math, vol.249, pp.74-94, 2013.

A. Chaillou and M. Suri, A posteriori estimation of the linearization error for strongly monotone nonlinear operators, J. Comput. Appl. Math, vol.205, pp.72-87, 2007.

L. Chesnel, C. Jr, and P. , T-coercivity and continuous Galerkin methods: application to transmission problems with sign changing coefficients, Numer. Math, vol.124, pp.1-29, 2013.
DOI : 10.1007/s00211-012-0510-8
URL : https://hal.archives-ouvertes.fr/hal-00688862

E. T. Chung, C. Jr, and P. , A staggered discontinuous Galerkin method for wave propagation in media with dielectrics and meta-materials, J. Comput. Appl. Math, vol.239, pp.189-207, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00697755

P. Ciarlet and M. Vohralík, Robust a posteriori error control for transmission problems with sign changing coefficients using localization of dual norms. HAL Preprint 01148476v1, 2015.

P. G. Ciarlet, The Finite Element Method for Elliptic Problems, of Studies in Mathematics and its Applications, vol.4, 1978.

A. Cohen, R. Devore, and R. H. Nochetto, Convergence rates of AFEM with H ?1 data, Found. Comput. Math, vol.12, pp.671-718, 2012.
DOI : 10.1007/s10208-012-9120-1
URL : http://www.math.umd.edu/%7Erhn/papers/pdf/afemH-1.pdf

P. Destuynder and B. Métivet, Explicit error bounds for a nonconforming finite element method, SIAM J. Numer. Anal, vol.35, pp.2099-2115, 1998.
DOI : 10.1137/s0036142996300191

P. Destuynder and B. Métivet, Explicit error bounds in a conforming finite element method, Math. Comp, vol.68, pp.1379-1396, 1999.
DOI : 10.1090/s0025-5718-99-01093-5
URL : http://www.ams.org/mcom/1999-68-228/S0025-5718-99-01093-5/S0025-5718-99-01093-5.pdf

D. Pietro, D. A. Ern, and A. , Mathematical aspects of discontinuous Galerkin methods, vol.69
URL : https://hal.archives-ouvertes.fr/hal-01820185

. Springer, , 2012.

V. Dolej?í, A. Ern, and M. Vohralík, hp-adaptation driven by polynomial-degree-robust a posteriori error estimates for elliptic problems, SIAM J. Sci. Comput, vol.38, pp.3220-3246, 2016.

L. El-alaoui, A. Ern, and M. Vohralík, Guaranteed and robust a posteriori error estimates and balancing discretization and linearization errors for monotone nonlinear problems, Comput. Methods Appl. Mech. Engrg, vol.200, pp.2782-2795, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00410471

A. Ern and J. Guermond, Theory and practice of finite elements, of Applied Mathematical Sciences, vol.159, 2004.

A. Ern and M. Vohralík, Adaptive inexact Newton methods with a posteriori stopping criteria for nonlinear diffusion PDEs, SIAM J. Sci. Comput, vol.35, pp.1761-1791, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00681422

A. Ern and M. Vohralík, Polynomial-degree-robust a posteriori estimates in a unified setting for conforming, nonconforming, discontinuous Galerkin, and mixed discretizations, SIAM J. Numer. Anal, vol.53, pp.1058-1081, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00921583

A. Ern and M. Vohralík, Stable broken H 1 and H(div) polynomial extensions for polynomialdegree-robust potential and flux reconstruction in three space dimensions, 2016.

D. W. Kelly, The self-equilibration of residuals and complementary a posteriori error estimates in the finite element method, Internat. J. Numer. Methods Engrg, vol.20, pp.1491-1506, 1984.

C. Kreuzer and E. Süli, Adaptive finite element approximation of steady flows of incompressible fluids with implicit power-law-like rheology, ESAIM Math. Model. Numer. Anal, vol.50, pp.1333-1369, 2016.

P. Ladevèze, L. , and D. , Error estimate procedure in the finite element method and applications, SIAM J. Numer. Anal, vol.20, pp.485-509, 1983.

R. Luce and B. I. Wohlmuth, A local a posteriori error estimator based on equilibrated fluxes, SIAM J. Numer. Anal, vol.42, pp.1394-1414, 2004.
URL : https://hal.archives-ouvertes.fr/inria-00343040

P. Morin, R. H. Nochetto, and K. G. Siebert, Local problems on stars: a posteriori error estimators, convergence, and performance, Math. Comp, vol.72, pp.1067-1097, 2003.

S. Nicaise and J. Venel, A posteriori error estimates for a finite element approximation of transmission problems with sign changing coefficients, J. Comput. Appl. Math, vol.235, pp.4272-4282, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00517989

S. Nicaise, K. Witowski, and B. I. Wohlmuth, An a posteriori error estimator for the Lamé equation based on equilibrated fluxes, IMA J. Numer. Anal, vol.28, pp.331-353, 2008.

L. E. Payne and H. F. Weinberger, An optimal Poincaré inequality for convex domains, Arch. Rational Mech. Anal, vol.5, pp.286-292, 1960.

W. Prager and J. L. Synge, Approximations in elasticity based on the concept of function space, Quart. Appl. Math, vol.5, pp.241-269, 1947.

S. Repin, A posteriori estimates for partial differential equations, of Radon Series on Computational and Applied Mathematics, vol.4, 2008.

J. E. Roberts, T. , and J. , Mixed and hybrid methods, Handbook of Numerical Analysis, vol.II, pp.523-639, 1991.
URL : https://hal.archives-ouvertes.fr/inria-00075815

A. Veeser, Approximating gradients with continuous piecewise polynomial functions, Found. Comput. Math, vol.16, pp.723-750, 2016.

A. Veeser and R. Verfürth, Explicit upper bounds for dual norms of residuals, SIAM J. Numer. Anal, vol.47, pp.2387-2405, 2009.

A. Veeser and R. Verfürth, Poincaré constants for finite element stars, IMA J. Numer. Anal, vol.32, pp.30-47, 2012.

R. Verfürth, A posteriori error estimates for non-linear parabolic equations, 2004.

R. Verfürth, Robust a posteriori error estimates for stationary convection-diffusion equations, SIAM J. Numer. Anal, vol.43, pp.1766-1782, 2005.

R. Verfürth, A posteriori error estimation techniques for finite element methods. Numerical Mathematics and Scientific Computation, 2013.

M. Vohralík, On the discrete Poincaré-Friedrichs inequalities for nonconforming approximations of the Sobolev space H 1, Numer. Funct. Anal. Optim, vol.26, pp.925-952, 2005.

M. Vohralík, Guaranteed and fully robust a posteriori error estimates for conforming discretizations of diffusion problems with discontinuous coefficients, J. Sci. Comput, vol.46, pp.397-438, 2011.

H. Wallen, H. Kettunen, and A. Sihvola, Surface modes of negative-parameter interfaces and the importance of rounding sharp corners, Metamaterials, vol.2, pp.113-121, 2008.