Y. Achdou, C. Bernardi, and F. Coquel, A priori and a posteriori analysis of finite volume discretizations of Darcy?s equations, Numerische Mathematik, vol.96, issue.1, pp.17-42, 2003.
DOI : 10.1007/s00211-002-0436-7

M. Ainsworth, A Posteriori Error Estimation for Lowest Order Raviart???Thomas Mixed Finite Elements, SIAM Journal on Scientific Computing, vol.30, issue.1, pp.189-204, 2007.
DOI : 10.1137/06067331X

A. Hassan, C. Japhet, M. Kern, and M. Vohralík, A posteriori stopping criteria for optimized Schwarz domain decomposition algorithms in mixed formulations, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01529532

T. Arbogast and Z. Chen, On the implementation of mixed methods as nonconforming methods for second-order elliptic problems, Math. Comp, vol.64, issue.211, pp.943-972, 1995.

M. Arioli, A stopping criterion for the conjugate gradient algorithm in a finite element method framework, Numerische Mathematik, vol.97, issue.1, pp.1-24, 2004.
DOI : 10.1007/s00211-003-0500-y

M. Arioli and D. Loghin, Stopping criteria for mixed finite element problems, Electron. Trans. Numer. Anal, vol.29, pp.178-19208, 2007.

D. N. Arnold and F. Brezzi, Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates, ESAIM: Mathematical Modelling and Numerical Analysis, vol.19, issue.1, pp.7-32, 1985.
DOI : 10.1051/m2an/1985190100071
URL : http://www.esaim-m2an.org/articles/m2an/pdf/1985/01/m2an1985190100071.pdf

R. Becker, C. Johnson, and R. Rannacher, Adapative Fehlerkontrolle f??r Finite-Elemente-Mehrgitter-Methoden, Computing, vol.54, issue.4, pp.271-288, 1995.
DOI : 10.1007/978-3-662-02427-0

D. Bennequin, M. J. Gander, and L. Halpern, A homographic best approximation problem with application to optimized Schwarz waveform relaxation, Mathematics of Computation, vol.78, issue.265, pp.78185-223, 2009.
DOI : 10.1090/S0025-5718-08-02145-5
URL : https://hal.archives-ouvertes.fr/hal-00111643

P. M. Berthe, C. Japhet, and P. Omnes, Space???Time Domain Decomposition with Finite Volumes for Porous Media Applications, Domain decomposition methods in science and engineering XXI, pp.483-490, 2014.
DOI : 10.1007/978-3-319-05789-7_54

E. Blayo, L. Debreu, and F. Lemarié, Toward an optimized global-in-time Schwarz algorithm for diffusion equations with discontinuous and spatially variable coefficients. Part 1: the constant coefficients case, pp.170-186, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00661978

E. Blayo, L. Halpern, and C. Japhet, Optimized Schwarz Waveform Relaxation Algorithms with Nonconforming Time Discretization for Coupling Convection-diffusion Problems with Discontinuous Coefficients, Domain decomposition methods in science and engineering XVI
DOI : 10.1007/978-3-540-34469-8_31
URL : https://hal.archives-ouvertes.fr/inria-00187555

E. Burman and A. Ern, Continuous interior penalty $hp$-finite element methods for advection and advection-diffusion equations, Mathematics of Computation, vol.76, issue.259, pp.1119-1140, 2007.
DOI : 10.1090/S0025-5718-07-01951-5
URL : http://www.ams.org/mcom/2007-76-259/S0025-5718-07-01951-5/S0025-5718-07-01951-5.pdf

C. Cancès, I. S. Pop, and M. Vohralík, An a posteriori error estimate for vertex-centered finite volume discretizations of immiscible incompressible two-phase flow, Mathematics of Computation, vol.83, issue.285, pp.153-188, 2014.
DOI : 10.1090/S0025-5718-2013-02723-8

P. Ciarlet, E. Jamelot, and F. D. Kpadonou, Domain decomposition methods for the diffusion equation with low-regularity solution, Computers & Mathematics with Applications, 2017.
DOI : 10.1016/j.camwa.2017.07.017
URL : https://hal.archives-ouvertes.fr/hal-01349385

L. C. Cowsar, J. Mandel, and M. F. Wheeler, Balancing domain decomposition for mixed finite elements, Mathematics of Computation, vol.64, issue.211, pp.989-1015, 1995.
DOI : 10.1090/S0025-5718-1995-1297465-9
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.44.1663

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

V. Dolean, P. Jolivet, and F. Nataf, An introduction to domain decomposition methods, Algorithms, theory, and parallel implementation, 2015.
DOI : 10.1137/1.9781611974065
URL : https://hal.archives-ouvertes.fr/cel-01100932

V. Dolej?í, A. Ern, and M. Vohralík, $hp$-Adaptation Driven by Polynomial-Degree-Robust A Posteriori Error Estimates for Elliptic Problems, SIAM Journal on Scientific Computing, vol.38, issue.5, pp.3220-3246, 2016.
DOI : 10.1137/15M1026687

J. Douglas, J. , P. J. Paes-leme, J. E. Roberts, and J. P. Wang, A parallel iterative procedure applicable to the approximate solution of second order partial differential equations by mixed finite element methods, Numerische Mathematik, vol.35, issue.1, pp.95-108, 1993.
DOI : 10.1007/BF01385742

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, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01377086

A. Ern and M. Vohralík, A Posteriori Error Estimation Based on Potential and Flux Reconstruction for the Heat Equation, SIAM Journal on Numerical Analysis, vol.48, issue.1, pp.198-223, 2010.
DOI : 10.1137/090759008
URL : https://hal.archives-ouvertes.fr/hal-00383692

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

C. Farhat and F. Roux, A method of finite element tearing and interconnecting and its parallel solution algorithm, International Journal for Numerical Methods in Engineering, vol.28, issue.6, pp.1205-1227, 1991.
DOI : 10.1016/B978-0-12-068650-6.50029-0

M. J. Gander, Optimized Schwarz Methods, SIAM Journal on Numerical Analysis, vol.44, issue.2, pp.699-731, 2006.
DOI : 10.1137/S0036142903425409
URL : https://hal.archives-ouvertes.fr/hal-00107263

M. J. Gander, L. Halpern, and M. Kern, A Schwarz Waveform Relaxation Method for Advection???Diffusion???Reaction Problems with Discontinuous Coefficients and Non-matching Grids, Lect. Notes Comput. Sci. Eng, vol.55, pp.283-290, 2007.
DOI : 10.1007/978-3-540-34469-8_33
URL : https://hal.archives-ouvertes.fr/hal-01111940

M. J. Gander, L. Halpern, and F. Nataf, Optimal Schwarz Waveform Relaxation for the One Dimensional Wave Equation, SIAM Journal on Numerical Analysis, vol.41, issue.5, pp.1643-1681, 2003.
DOI : 10.1137/S003614290139559X
URL : https://archive-ouverte.unige.ch/unige:6285/ATTACHMENT01

M. J. Gander and C. Japhet, Algorithm 932, ACM Transactions on Mathematical Software, vol.40, issue.1, 2013.
DOI : 10.1145/2513109.2513115
URL : https://hal.archives-ouvertes.fr/hal-00933643

M. J. Gander, C. Japhet, Y. Maday, and F. Nataf, A New Cement to Glue Nonconforming Grids with Robin Interface Conditions: The Finite Element Case, Domain decomposition methods in science and engineering, pp.259-266, 2005.
DOI : 10.1007/3-540-26825-1_24
URL : https://hal.archives-ouvertes.fr/hal-00112937

F. Haeberlein, Time Space Domain Decomposition Methods for Reactive Transport ? Application to CO2 Geological Storage, 2011.
DOI : 10.1016/j.procs.2010.04.081
URL : https://hal.archives-ouvertes.fr/tel-00634507

F. Haeberlein, L. Halpern, and A. Michel, Newton-Schwarz Optimised Waveform Relaxation Krylov Accelerators for Nonlinear Reactive Transport, Lect. Notes Comput. Sci. Eng, vol.91, pp.387-394, 2013.
DOI : 10.1007/978-3-642-35275-1_45

L. Halpern, C. Japhet, and J. Szeftel, Discontinuous Galerkin and Nonconforming in Time Optimized Schwarz Waveform Relaxation, In Domain Decomposition Methods in Science and Engineering XIX Lect. Notes Comput. Sci. Eng, vol.78, pp.133-140, 2011.
DOI : 10.1007/978-3-642-11304-8_13

L. Halpern, C. Japhet, and J. Szeftel, Optimized Schwarz Waveform Relaxation and Discontinuous Galerkin Time Stepping for Heterogeneous Problems, SIAM Journal on Numerical Analysis, vol.50, issue.5, pp.2588-2611, 2012.
DOI : 10.1137/120865033
URL : https://hal.archives-ouvertes.fr/hal-00479814

T. Hoang, J. Jaffré, C. Japhet, M. Kern, and J. E. Roberts, Space-Time Domain Decomposition Methods for Diffusion Problems in Mixed Formulations, SIAM Journal on Numerical Analysis, vol.51, issue.6, pp.3532-3559, 2013.
DOI : 10.1137/130914401
URL : https://hal.archives-ouvertes.fr/hal-00803796

T. Hoang, C. Japhet, M. Kern, and J. E. Roberts, Space-Time Domain Decomposition for Reduced Fracture Models in Mixed Formulation, SIAM Journal on Numerical Analysis, vol.54, issue.1, pp.288-316, 2016.
DOI : 10.1137/15M1009651

T. T. Hoang, C. Japhet, M. Kern, and J. E. Roberts, Space???time domain decomposition for advection???diffusion problems in mixed formulations, Mathematics and Computers in Simulation, vol.137, pp.366-389, 2017.
DOI : 10.1016/j.matcom.2016.11.002
URL : https://hal.archives-ouvertes.fr/hal-01296348

C. Japhet and F. Nataf, The best interface conditions for domain decomposition methods: absorbing boundary conditions, Absorbing Boundaries and Layers, Domain Decomposition Methods, pp.348-373, 2001.

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

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

K. Y. Kim, A posteriori error analysis for locally conservative mixed methods, Mathematics of Computation, vol.76, issue.257, pp.43-66, 2007.
DOI : 10.1090/S0025-5718-06-01903-X
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.2285

P. Ladevèze and J. Pelle, Mastering calculations in linear and nonlinear mechanics. Mechanical Engineering Series, 2005.

P. Lions, R. G. Chan, and O. Widlund, On the Schwarz alternating method III: a variant for nonoverlapping subdomains, Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, pp.202-223, 1989.

J. Mandel, Balancing domain decomposition, Communications in Numerical Methods in Engineering, vol.13, issue.3, pp.233-241, 1993.
DOI : 10.1137/1.9781611971057.ch5
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.44.876

V. Martin, An optimized Schwarz waveform relaxation method for the unsteady convection diffusion equation in two dimensions, Applied Numerical Mathematics, vol.52, issue.4, pp.401-428, 2005.
DOI : 10.1016/j.apnum.2004.08.022

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

A. T. Patera and E. M. Rønquist, A GENERAL OUTPUT BOUND RESULT: APPLICATION TO DISCRETIZATION AND ITERATION ERROR ESTIMATION AND CONTROL, Mathematical Models and Methods in Applied Sciences, vol.11, issue.04, pp.685-712, 2001.
DOI : 10.1016/S0045-7825(98)00244-8

G. V. Pencheva, M. Vohralík, M. F. Wheeler, and T. Wildey, Robust a Posteriori Error Control and Adaptivity for Multiscale, Multinumerics, and Mortar Coupling, SIAM Journal on Numerical Analysis, vol.51, issue.1, pp.526-554, 2013.
DOI : 10.1137/110839047
URL : https://hal.archives-ouvertes.fr/hal-00467738

W. Prager and J. L. Synge, Approximations in elasticity based on the concept of function space, Quarterly of Applied Mathematics, vol.5, issue.3, pp.241-269, 1947.
DOI : 10.1090/qam/25902

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

V. Rey, P. Gosselet, and C. Rey, Strict bounding of quantities of interest in computations based on domain decomposition, Computer Methods in Applied Mechanics and Engineering, vol.287, pp.212-228, 2015.
DOI : 10.1016/j.cma.2015.01.009
URL : https://hal.archives-ouvertes.fr/hal-01113852

V. Rey, P. Gosselet, and C. Rey, Strict lower bounds with separation of sources of error in non-overlapping domain decomposition methods, International Journal for Numerical Methods in Engineering, vol.155, issue.1-2, pp.1007-1029, 2016.
DOI : 10.1016/S0045-7825(97)00146-1
URL : https://hal.archives-ouvertes.fr/hal-01332674

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, Computer Methods in Applied Mechanics and Engineering, vol.270, pp.293-303, 2014.
DOI : 10.1016/j.cma.2013.12.001
URL : https://hal.archives-ouvertes.fr/hal-00919435

V. Thomee, Galerkin Finite Element Methods for Parabolic Problems, 1997.
DOI : 10.1007/978-3-662-03359-3

R. Verfürth, A posteriori error estimates for finite element discretizations of the heat equation, Calcolo, vol.40, issue.3, pp.195-212, 2003.
DOI : 10.1007/s10092-003-0073-2

M. Vohralík, A Posteriori Error Estimates for Lowest-Order Mixed Finite Element Discretizations of Convection-Diffusion-Reaction Equations, SIAM Journal on Numerical Analysis, vol.45, issue.4, pp.1570-1599, 2007.
DOI : 10.1137/060653184

M. Vohralík, Unified primal formulation-based a priori and a posteriori error analysis of mixed finite element methods, Mathematics of Computation, vol.79, issue.272, pp.2001-2032, 2010.
DOI : 10.1090/S0025-5718-2010-02375-0