W. Gui and I. Babu?ka, The h, p and h-p versions of the finite element method in 1 dimension. II. The error analysis of the h-and h-p versions, Numer. Math, vol.49, issue.6, pp.613-657, 1986.

W. Gui and I. Babu?ka, The h, p and h-p versions of the finite element method in 1 dimension. III. The adaptive h-p version, Numer. Math, vol.49, issue.6, pp.659-683, 1986.

I. Babu?ka and B. Guo, The h-p version of finite element method, part 1: The basic approximation results, Comp. Mech, issue.1, pp.21-41, 1986.

I. Babu?ka and B. Guo, The h-p version of finite element method, part 2: General results and application, Comp. Mech, issue.1, pp.203-220, 1986.

R. H. Nochetto, K. G. Siebert, and A. Veeser, Theory of adaptive finite element methods: an introduction, Multiscale, nonlinear and adaptive approximation, pp.409-542, 2009.

R. Stevenson, An optimal adaptive finite element method, SIAM J. Numer. Anal, vol.42, issue.5, pp.2188-2217, 2005.

R. Stevenson, Optimality of a standard adaptive finite element method, Found, Comput. Math, vol.7, issue.2, pp.245-269, 2007.

M. Arioli, E. H. Georgoulis, and D. Loghin, Stopping criteria for adaptive finite element solvers, SIAM, J. Sci. Comput, vol.35, issue.3, 2013.
DOI : 10.1137/120867421

M. Arioli, J. Liesen, A. Mi-'-edlar, and Z. Strako?, Interplay between discretization and algebraic computation in adaptive numerical solution of elliptic PDE problems, GAMM-Mitt, vol.36, issue.1, pp.102-129, 2013.

M. Holst, R. Szypowski, and Y. Zhu, Adaptive finite element methods with inexact solvers for the nonlinear Poisson-Boltzmann equation, Domain decomposition methods in science and engineering XX, vol.91, pp.167-174, 2013.

C. Carstensen, M. Feischl, M. Page, and D. Praetorius, Axioms of adaptivity, Comput. Math. Appl, vol.67, issue.6, pp.1195-1253, 2014.
DOI : 10.1016/j.camwa.2013.12.003

URL : https://doi.org/10.1016/j.camwa.2013.12.003

G. Gantner, A. Haberl, D. Praetorius, and B. Stiftner, Rate optimal adaptive FEM with inexact solver for nonlinear operators, IMA J. Numer. Anal, 2017.

R. Becker, C. Johnson, and R. Rannacher, Adaptive error control for multigrid finite element methods, Computing, vol.55, issue.4, pp.271-288, 1995.
DOI : 10.1007/bf02238483

A. Ern and M. Vohralík, Adaptive inexact Newton methods with a posteriori stopping criteria for nonlinear diffusion PDEs, SIAM J. Sci. Comput, vol.35, issue.4, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00681422

P. Daniel, A. Ern, I. Smears, and M. Vohralík, An adaptive hp-refinement strategy with computable guaranteed bound on the error reduction factor, Computers and Mathematics with Applica, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01666763

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, issue.5, 2016.

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, p.1662944, 2017.

W. Dörfler, A convergent adaptive algorithm for Poisson's equation, SIAM J. Numer. Anal, vol.33, issue.3, pp.1106-1124, 1996.

J. Pape?, Z. Strako?, and M. Vohralík, Estimating and localizing the algebraic and total numerical errors using flux reconstructions, Numer. Math, vol.138, issue.3, pp.681-721, 2018.

P. Destuynder and B. Métivet, Explicit error bounds in a conforming finite element method, Math. Comp, vol.68, issue.228, pp.1379-1396, 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.

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, issue.2, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00921583

A. Ern and M. Vohralík, Stable broken H 1 and H(div) polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions, HAL Preprint, p.1422204, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01422204

P. Jiránek, Z. Strako?, and M. Vohralík, A posteriori error estimates including algebraic error and stopping criteria for iterative solvers, SIAM J. Sci. Comput, vol.32, issue.3, 2010.

V. Rey, C. Rey, and P. Gosselet, A strict error bound with separated contributions of the discretization and of the iterative solver in non-overlapping domain decomposition methods, Comput. Methods Appl. Mech. Engrg, vol.270, pp.293-303, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00919435

I. Babu?ka and T. Strouboulis, The finite element method and its reliability, Numerical Mathematics and Scientific Computation, 2001.

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

F. Brezzi and M. Fortin, Springer Series in Computational Mathematics, vol.15, 1991.

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

E. G. Sewell, Automatic generation of triangulations for piecewise polynomial approximation, ProQuest LLC, 1972.

W. F. Mitchell, A comparison of adaptive refinement techniques for elliptic problems, ACM Trans. Math. Software, vol.15, issue.4, pp.326-347, 1989.

P. Morin, R. H. Nochetto, and K. G. Siebert, revised reprint of "Data oscillation and convergence of adaptive FEM, SIAM J. Numer. Anal, vol.44, issue.4, pp.466-488, 2000.

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

W. F. Mitchell and M. A. Mcclain, A comparison of hp-adaptive strategies for elliptic partial differential equations (long version, 2011.

B. Szabó and I. Babu?ka, Finite element analysis, 1991.

P. Ciarlet and M. Vohralík, Localization of global norms and robust a posteriori error control for transmission problems with sign-changing coefficients, M2AN Math. Model. Numer. Anal, vol.52, issue.5, pp.2037-2064, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01148476

E. Cancès, G. Dusson, Y. Maday, B. Stamm, and M. Vohralík, Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: conforming approximations, SIAM J. Numer. Anal, vol.55, issue.5, pp.2228-2254, 2017.

I. Smears and M. Vohralík, Simple and robust equilibrated flux a posteriori estimates for singularly perturbed reaction-diffusion problems, HAL Preprint 01956180, 2018.

G. Mallik, M. Vohralík, and S. Yousef, Goal-oriented a posteriori error estimation for conforming and nonconforming approximations with inexact solvers, HAL Preprint 01964733, 2018.

A. Ern, I. Smears, and M. Vohralík, Guaranteed, locally space-time efficient, and polynomial-degree robust a posteriori error estimates for high-order discretizations of parabolic problems, SIAM J. Numer. Anal, vol.55, issue.6, pp.2811-2834, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01377086