M. Aganagi´caganagi´c, Newton's method for linear complementarity problems, Math. Programming, pp.349-362, 1984.

M. Ainsworth and J. T. Oden, A posteriori error estimation in finite element analysis, Pure and Applied Mathematics, 2000.

M. Arioli, E. H. Georgoulis, and D. Loghin, Stopping Criteria for Adaptive Finite Element Solvers, SIAM Journal on Scientific Computing, vol.35, issue.3, pp.1537-1559, 2013.
DOI : 10.1137/120867421
URL : http://web.mat.bham.ac.uk/loghin/agl2013.pdf

M. Bebendorf, A Note on the Poincar?? Inequality for Convex Domains, Zeitschrift f??r Analysis und ihre Anwendungen, vol.22, pp.751-756, 2003.
DOI : 10.4171/ZAA/1170

F. B. Belgacem, C. Bernardi, A. Blouza, and M. Vohralík, A finite element discretization of the contact between two membranes, ESAIM: Mathematical Modelling and Numerical Analysis, vol.33, issue.1, pp.33-52, 2008.
DOI : 10.1007/s10915-007-9139-7

F. B. Belgacem, C. Bernardi, A. Blouza, and M. Vohralík, On the Unilateral Contact Between Membranes. Part 1: Finite Element Discretization and Mixed Reformulation, Mathematical Modelling of Natural Phenomena, vol.346, issue.1, pp.21-43, 2009.
DOI : 10.1016/j.crma.2008.03.006
URL : https://hal.archives-ouvertes.fr/hal-00461144

F. B. Belgacem, C. Bernardi, A. Blouza, and M. Vohralík, On the unilateral contact between membranes. Part 2: a posteriori analysis and numerical experiments, IMA Journal of Numerical Analysis, vol.32, issue.3, pp.1147-1172, 2012.
DOI : 10.1093/imanum/drr003
URL : https://hal.archives-ouvertes.fr/hal-00461144

I. , B. Gharbia, and J. Jaffré, Gas phase appearance and disappearance as a problem with complementarity constraints, Math. Comput. Simulation, pp.99-127, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00641621

D. Braess, V. Pillwein, and J. Schöberl, Equilibrated residual error estimates are p-robust, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.13-14, pp.1189-1197, 2009.
DOI : 10.1016/j.cma.2008.12.010

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

F. Brezzi and M. Fortin, Mixed and hybrid finite element methods, pp.978-979, 1991.
DOI : 10.1007/978-1-4612-3172-1

C. Carstensen and S. A. Funken, Fully Reliable Localized Error Control in the FEM, SIAM Journal on Scientific Computing, vol.21, issue.4, pp.1465-1484, 1999.
DOI : 10.1137/S1064827597327486

Z. Chen, Finite element methods and their applications, Scientific Computation, 2005.

F. H. Clarke, Optimization and nonsmooth analysis Series of Monographs and Advanced Texts, 1983.

D. Luca, F. Facchinei, and C. Kanzow, A semismooth equation approach to the solution of nonlinear complementarity problems, Math. Programming, vol.75, pp.407-439, 1996.

P. Destuynder and B. Métivet, Explicit error bounds in a conforming finite element method, Mathematics of Computation, vol.68, issue.228, pp.1379-1396, 1999.
DOI : 10.1090/S0025-5718-99-01093-5

D. A. Di-pietro, E. Flauraud, M. Vohralík, and S. Yousef, A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media, Journal of Computational Physics, vol.276, pp.163-187, 2014.
DOI : 10.1016/j.jcp.2014.06.061
URL : https://hal.archives-ouvertes.fr/hal-00839487

S. C. Eisenstat and H. F. Walker, Globally Convergent Inexact Newton Methods, SIAM Journal on Optimization, vol.4, issue.2, pp.393-422, 1994.
DOI : 10.1137/0804022
URL : http://users.wpi.edu/~walker/Papers/global_inexact_newton,SIOPT_4,1994,393-422.pdf

A. Ern and M. Vohralík, Adaptive Inexact Newton Methods with A Posteriori Stopping Criteria for Nonlinear Diffusion PDEs, SIAM Journal on Scientific Computing, vol.35, issue.4, pp.1761-1791, 2013.
DOI : 10.1137/120896918
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 Journal on Numerical Analysis, vol.53, issue.2, pp.1058-1081, 2015.
DOI : 10.1137/130950100
URL : https://hal.archives-ouvertes.fr/hal-00921583

F. Facchinei and C. Kanzow, A nonsmooth inexact Newton method for the solution of large-scale nonlinear complementarity problems, Mathematical Programming, vol.77, issue.3, pp.493-512, 1997.
DOI : 10.1007/978-3-642-68874-4_14

F. Facchinei, C. Kanzow, and S. Sagratella, Solving quasi-variational inequalities via their KKT conditions, Mathematical Programming, vol.47, issue.1-2, pp.369-412, 2014.
DOI : 10.1287/opre.47.1.102

F. Facchinei and J. Pang, Finite-dimensional variational inequalities and complementarity problems, 2003.

Z. Ge, Q. Ni, and X. Zhang, A smoothing inexact Newton method for variational inequalities with nonlinear constraints, Journal of Inequalities and Applications, vol.26, issue.1, p.12, 2017.
DOI : 10.1007/BF02591868

M. Hintermüller, K. Ito, and K. Kunisch, The Primal-Dual Active Set Strategy as a Semismooth Newton Method, SIAM Journal on Optimization, vol.13, issue.3, pp.865-888, 2002.
DOI : 10.1137/S1052623401383558

I. Hlavá?ek, J. Haslinger, J. Ne?as, and J. Loví?ek, Solution of variational inequalities in mechanics, Applied Mathematical Sciences, vol.66, pp.978-979, 1988.
DOI : 10.1007/978-1-4612-1048-1

P. Jiránek, Z. Strako?, and M. Vohralík, A Posteriori Error Estimates Including Algebraic Error and Stopping Criteria for Iterative Solvers, SIAM Journal on Scientific Computing, vol.32, issue.3, pp.1567-1590, 2010.
DOI : 10.1137/08073706X

C. Kanzow, An Active Set-Type Newton Method for Constrained Nonlinear Systems, Complementarity: applications, algorithms and extensions, pp.179-200978, 1999.
DOI : 10.1007/978-1-4757-3279-5_9
URL : http://www.math.uni-hamburg.de/home/kanzow/CNS.ps.Z

C. Kanzow, Inexact semismooth Newton methods for large-scale complementarity problems, The First International Conference on Optimization Methods and Software. Part II, pp.309-325, 2004.
DOI : 10.1007/BF00247654

C. T. Kelley, Iterative methods for linear and nonlinear equations, Frontiers in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), vol.16, 1995.
DOI : 10.1137/1.9781611970944

R. Kornhuber, A posteriori error estimates for elliptic variational inequalities, Computers & Mathematics with Applications, vol.31, issue.8, pp.31-49, 1996.
DOI : 10.1016/0898-1221(96)00030-2
URL : https://doi.org/10.1016/0898-1221(96)00030-2

J. Lions and G. Stampacchia, Variational inequalities, Communications on Pure and Applied Mathematics, vol.15, issue.3, pp.493-519, 1967.
DOI : 10.5802/aif.204

J. M. Martínez and L. Q. Qi, Inexact Newton methods for solving nonsmooth equations, Linear/nonlinear iterative methods and verification of solution, pp.127-145, 1993.
DOI : 10.1016/0377-0427(94)00088-I

D. Meidner, R. Rannacher, and J. Vihharev, Goal-oriented error control of the iterative solution of finite element equations, Journal of Numerical Mathematics, vol.4, issue.2, pp.143-172, 2009.
DOI : 10.1137/S003614299732334X

J. Pape?, U. Rüde, M. Vohralík, and B. Wohlmuth, Sharp algebraic and total a posteriori error bounds for h and p finite elements via a multilevel approach. HAL Preprint 01662944, submitted for publication, 2017.

L. E. Payne and H. F. Weinberger, An optimal Poincar?? inequality for convex domains, Archive for Rational Mechanics and Analysis, vol.5, issue.1, pp.286-292, 1960.
DOI : 10.2140/pjm.1958.8.551

P. Raviart and J. Thomas, A mixed finite element method for 2-nd order elliptic problems, Proc. Conf., Consiglio Naz, pp.292-315, 1975.
DOI : 10.1007/BF01436186

S. Repin, A posteriori estimates for partial differential equations, Radon Series on Computational and Applied Mathematics, vol.4, 2008.
DOI : 10.1515/9783110203042

S. I. Repin, Functional a posteriori estimates for elliptic variational inequalities, Journal of Mathematical Sciences, vol.138, issue.230, pp.147-164, 2007.
DOI : 10.1090/S0025-5718-99-01190-4

J. Rodrigues, Obstacle problems in mathematical physics, p.114, 1987.

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

S. J. Wright, Primal-dual interior-point methods, Society for Industrial and Applied Mathematics (SIAM), 1997.
DOI : 10.1137/1.9781611971453
URL : http://www.cs.wisc.edu/~swright/papers/potra-wright.ps