M. Ainsworth and R. Rankin, Fully computable bounds for the error in nonconforming finite element approximations of arbitrary order on triangular elements, SIAM J. Numer. Anal, vol.46, pp.3207-3232, 2008.

, Guaranteed computable bounds on quantities of interest in finite element computations, Internat. J. Numer. Methods Engrg, vol.89, pp.1605-1634, 2012.

W. Bangerth and R. Rannacher, Adaptive finite element methods for differential equations, Lectures in Mathematics ETH Zürich, 2003.

R. Becker, C. Johnson, and R. Rannacher, Adaptive error control for multigrid finite element methods, Computing, vol.55, pp.271-288, 1995.

R. Becker and R. Rannacher, An optimal control approach to a posteriori error estimation in finite element methods, Acta Numer, vol.10, pp.1-102, 2001.

D. Braess and J. Schöberl, Equilibrated residual error estimator for edge elements, Math. Comp, vol.77, pp.651-672, 2008.

M. Bürg and M. Nazarov, Goal-oriented adaptive finite element methods for elliptic problems revisited, J. Comput. Appl. Math, vol.287, pp.125-147, 2015.

J. H. Chaudhry, E. C. Cyr, K. Liu, T. A. Manteuffel, L. N. Olson et al., Enhancing least-squares finite element methods through a quantity-of-interest, SIAM J. Numer. Anal, vol.52, pp.3085-3105, 2014.

M. Christie and M. Blunt, Tenth SPE comparative solution project: A comparison of upscaling techniques, SPE Reservoir Simulation Symposium, 2001.

P. Destuynder and B. Métivet, Explicit error bounds in a conforming finite element method, Math. Comp, vol.68, pp.1379-1396, 1999.

D. A. Di-pietro and A. Ern, of Mathématiques & Applications (Berlin) [Mathematics & Applications, vol.69, 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.

V. Dolej?í and F. Roskovec, Goal-oriented error estimates including algebraic errors in discontinuous Galerkin discretizations of linear boundary value problems, Appl. Math, vol.62, pp.579-605, 2017.

V. Dolej?í, I. ?ebestová, and M. Vohralík, Algebraic and discretization error estimation by equilibrated fluxes for discontinuous Galerkin methods on nonmatching grids, J. Sci. Comput, vol.64, pp.1-34, 2015.

V. Dolej?í, G. May, A. Rangarajan, and F. Roskovec, A goal-oriented high-order anisotropic mesh adaptation using discontinuous Galerkin method for linear convectiondiffusion-reaction problems, SIAM J. Sci. Comput, vol.41, pp.1899-1922, 2019.

B. Endtmayer and T. Wick, A partition-of-unity dual-weighted residual approach for multiobjective goal functional error estimation applied to elliptic problems, Comput. Methods Appl. Math, vol.17, pp.575-599, 2017.

A. Ern, S. Nicaise, and M. Vohralík, An accurate H(div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems, C. R. Math. Acad. Sci, vol.345, pp.709-712, 2007.

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

, Four closely related equilibrated flux reconstructions for nonconforming finite elements, C. R. Math. Acad. Sci. Paris, pp.77-80, 2013.

, 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.

R. Eymard, T. Gallouët, and R. Herbin, Handbook of Numerical Analysis, vol.VII, pp.713-1020, 2000.

M. B. Giles and E. Süli, Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality, Acta Numer, vol.11, pp.145-236, 2002.

R. Hartmann, Multitarget error estimation and adaptivity in aerodynamic flow simulations, SIAM J. Sci. Comput, vol.31, pp.708-731, 2008.

M. Holst and S. Pollock, Convergence of goal-oriented adaptive finite element methods for nonsymmetric problems, Numer. Methods Partial Differential Equations, vol.32, pp.479-509, 2016.

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, pp.1567-1590, 2010.

O. A. Karakashian and F. Pascal, A posteriori error estimates for a discontinuous Galerkin approximation of second-order elliptic problems, SIAM J. Numer. Anal, vol.41, pp.2374-2399, 2003.

K. Kergrene, S. Prudhomme, L. Chamoin, and M. Laforest, A new goal-oriented formulation of the finite element method, Comput. Methods Appl. Mech. Engrg, vol.327, pp.256-276, 2017.

P. Ladevèze, Strict upper error bounds on computed outputs of interest in computational structural mechanics, Comput. Mech, vol.42, pp.271-286, 2008.

P. Ladevèze and L. Chamoin, Calculation of strict error bounds for finite element approximations of non-linear pointwise quantities of interest, Internat. J. Numer. Methods Engrg, vol.84, pp.1638-1664, 2010.

P. Ladevèze, F. Pled, and L. Chamoin, New bounding techniques for goal-oriented error estimation applied to linear problems, Internat. J. Numer. Methods Engrg, vol.93, pp.1345-1380, 2013.

Y. Maday and A. T. Patera, Numerical analysis of a posteriori finite element bounds for linear functional outputs, Math. Models Methods Appl. Sci, vol.10, pp.785-799, 2000.

D. Meidner, R. Rannacher, and J. Vihharev, Goal-oriented error control of the iterative solution of finite element equations, J. Numer. Math, vol.17, pp.143-172, 2009.

M. S. Mommer and R. Stevenson, A goal-oriented adaptive finite element method with convergence rates, SIAM J. Numer. Anal, vol.47, pp.861-886, 2009.

I. Mozolevski and S. Prudhomme, Goal-oriented error estimation based on equilibratedflux reconstruction for finite element approximations of elliptic problems, Comput. Methods Appl. Mech. Engrg, vol.288, pp.127-145, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00985971

J. Nédélec, Mixed finite elements in R 3, Numer. Math, vol.35, pp.315-341, 1980.

J. T. Oden and S. Prudhomme, Goal-oriented error estimation and adaptivity for the finite element method, Comput. Math. Appl, vol.41, pp.735-756, 2001.

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, 2017.

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

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. Prudhomme and J. T. Oden, On goal-oriented error estimation for elliptic problems: application to the control of pointwise errors, New advances in computational methods, vol.176, pp.313-331, 1997.

P. Raviart and J. Thomas, A mixed finite element method for 2nd order elliptic problems, Mathematical aspects of finite element methods (Proc. Conf., Consiglio Naz. delle Ricerche, vol.606, pp.292-315, 1975.

V. Rey, P. Gosselet, and C. Rey, Strict bounding of quantities of interest in computations based on domain decomposition, Comput. Methods Appl. Mech. Engrg, vol.287, pp.212-228, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01113852

, Strict lower bounds with separation of sources of error in non-overlapping domain decomposition methods, Internat. J. Numer. Methods Engrg, vol.108, pp.1007-1029, 2016.

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

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. H. Van-brummelen, S. Zhuk, and G. J. Van-zwieten, Worst-case multi-objective error estimation and adaptivity, Comput. Methods Appl. Mech. Engrg, vol.313, pp.723-743, 2017.

H. A. Van-der and . Vorst, Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Statist. Comput, vol.13, pp.631-644, 1992.

M. Vohralík and S. Yousef, A simple a posteriori estimate on general polytopal meshes with applications to complex porous media flows, Comput. Methods Appl. Mech. Engrg, vol.331, pp.728-760, 2018.