. Akrivis, Optimal order a posteriori error estimates for a class of Runge-Kutta and Galerkin methods, Numer. Math, vol.114, pp.133-160, 2009.

M. Amrein-&-wihler-;-amrein and T. P. Wihler, An adaptive spacetime Newton-Galerkin approach for semilinear singularly perturbed parabolic evolution equations, IMA J. Numer. Anal, vol.37, 2004.

. Bergam, A posteriori analysis of the finite element discretization of some parabolic equations, Math. Comp, vol.74, pp.1117-1138, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00020615

. Braess, 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

Z. Chen-&-feng-;-chen and J. Feng, An adaptive finite element algorithm with reliable and efficient error control for linear parabolic problems, Math. Comp, vol.73, pp.1167-1193, 2004.

M. Costabel-&-mcintosh-;-costabel and A. Mcintosh, On Bogovski? ? and regularized Poincaré integral operators for de Rham complexes on Lipschitz domains, Math. Z, vol.265, pp.297-320, 2010.

P. Di, Adaptive regularization, linearization, and discretization and a posteriori error control for the two-phase Stefan problem, Math. Comp, vol.84, pp.153-186, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00690862

. Dolej?í, A framework for robust a posteriori error control in unsteady nonlinear advection-diffusion problems, SIAM J. Numer. Anal, vol.51, pp.773-793, 2013.

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

K. Eriksson-&-johnson-;-eriksson and C. Johnson, Adaptive finite element methods for parabolic problems. II. Optimal error estimates in L ? L 2 and L ? L ?, SIAM J. Numer. Anal, vol.32, pp.706-740, 1995.

A. Ern, I. Smears, and M. Vohralík, Discrete p-robust discrete p-robust H(div)-liftings and a posteriori error analysis of elliptic problems with H ?1 source terms. Calcolo, vol.54, pp.1009-1025, 2017.

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

A. Ern and F. Schieweck, Discontinuous Galerkin method in time combined with a stabilized finite element method in space for linear first-order PDEs, Math. Comp, vol.85, pp.2099-2129, 2016.
URL : https://hal.archives-ouvertes.fr/hal-00947695

A. Ern and M. Vohralík, A posteriori error estimation based on potential and flux reconstruction for the heat equation, SIAM J. Numer. Anal, vol.48, pp.198-223, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00383692

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 polynomial-degree-robust potential and flux reconstruction in three space dimensions. Submitted for publication, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01422204

[. Gaspoz, A convergent time-space adaptive dG(s) finite element method for parabolic problems motivated by equal error distribution. Submitted for publication, 2016.

. Georgoulis, A posteriori error control for discontinuous Galerkin methods for parabolic problems, SIAM J. Numer. Anal, vol.49, pp.427-458, 2011.
DOI : 10.1137/080722461
URL : http://arxiv.org/pdf/0804.4262

. Georgoulis, A posteriori error bounds for fully-discrete hp-discontinuous Galerkin timestepping methods for parabolic problems, 2017.
DOI : 10.1007/978-3-642-11795-4_37
URL : http://arxiv.org/pdf/1001.2935

[. Kreuzer, Design and convergence analysis for an adaptive discretization of the heat equation, IMA J. Numer. Anal, vol.32, pp.1375-1403, 2012.

C. Kreuzer, Reliable and efficient a posteriori error estimates for finite element approximations of the parabolic p-Laplacian, Calcolo, vol.50, pp.79-110, 2013.

O. Lakkis and C. Makridakis, Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems, Math. Comp, vol.75, pp.1627-1658, 2006.
DOI : 10.1090/s0025-5718-06-01858-8
URL : https://www.ams.org/mcom/2006-75-256/S0025-5718-06-01858-8/S0025-5718-06-01858-8.pdf

C. Makridakis-&-nochetto-;-makridakis and R. H. Nochetto, Elliptic reconstruction and a posteriori error estimates for parabolic problems, SIAM J. Numer. Anal, vol.41, pp.1585-1594, 2003.

C. Makridakis and R. H. Nochetto, A posteriori error analysis for higher order dissipative methods for evolution problems, Numer. Math, vol.104, pp.489-514, 2006.
DOI : 10.1007/s00211-006-0013-6
URL : http://www.math.umd.edu/~rhn/papers/pdf/higher.pdf

S. Nicaise and N. Soualem, A posteriori error estimates for a nonconforming finite element discretization of the heat equation, M2AN Math. Model. Numer. Anal, vol.39, pp.319-348, 2005.

[. Nochetto, Theory of adaptive finite element methods: an introduction. Multiscale, nonlinear and adaptive approximation, pp.409-542, 2009.

M. Picasso, Adaptive finite elements for a linear parabolic problem, Comput. Methods Appl. Mech. Engrg, vol.167, pp.223-237, 1998.
DOI : 10.1016/s0045-7825(98)00121-2

S. Repin, Estimates of deviations from exact solutions of initialboundary value problem for the heat equation, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei, vol.13, issue.9, pp.121-133, 2002.

D. Schötzau and T. P. Wihler, A posteriori error estimation for hp-version time-stepping methods for parabolic partial differential equations, Numer. Math, vol.115, pp.475-509, 2010.

C. Schwab, p-and hp-finite element methods. Numerical Mathematics and Scientific Computation, p.374, 1998.

I. Smears, Robust and efficient preconditioners for the discontinuous Galerkin time-stepping method, IMA J. Numer. Anal, vol.37, 1961.
DOI : 10.1093/imanum/drw050
URL : https://hal.archives-ouvertes.fr/hal-01357497

F. Tantardini-&-veeser-;-tantardini and A. Veeser, The L 2-projection and quasi-optimality of Galerkin methods for parabolic equations, SIAM J. Numer. Anal, vol.54, pp.317-340, 2016.

R. Verfürth, A posteriori error estimates for nonlinear problems. L r (0, T ; L ? (?))-error estimates for finite element discretizations of parabolic equations, Math. Comp, vol.67, pp.1335-1360, 1998.

R. Verfürth, A posteriori error estimates for nonlinear problems: L r (0, T ; W 1,? (?))-error estimates for finite element discretizations of parabolic equations, Numer. Methods Partial Differential Equations, vol.14, pp.487-518, 1998.

R. Verfürth, A posteriori error estimates for finite element discretizations of the heat equation, Calcolo, vol.40, pp.195-212, 2003.

R. Verfürth, A posteriori error estimation techniques for finite element methods. Numerical Mathematics and Scientific Computation, p.393, 2013.

J. Wloka, Partial differential equations, p.518, 1987.