A posteriori error estimation in finite element analysis, Pure and Applied Mathematics, 2000. ,
Modeling compositional compressible two-phase flow in porous media by the concept of the global pressure, Comput. Geosci, vol.18, issue.3-4, pp.297-309, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00868281
Boundary value problems in mechanics of nonhomogeneous fluids, Studies in Mathematics and its Applications, vol.22, 1990. ,
The existence of weak solutions to single porosity and simple dual-porosity models of two-phase incompressible flow, Nonlinear Anal, vol.19, issue.11, pp.1009-1031, 1992. ,
Stopping criteria for adaptive finite element solvers, SIAM J. Sci. Comput, vol.35, issue.3, pp.1537-1559, 2013. ,
Numerical computation of multiphase flow in porous media, 1999. ,
A note on the Poincaré inequality for convex domains, Z. Anal. Anwendungen, vol.22, issue.4, pp.751-756, 2003. ,
On the unilateral contact between membranes. Part 2: a posteriori analysis and numerical experiments, IMA J. Numer. Anal, vol.32, issue.3, pp.1147-1172, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00461144
Nonconvergence of the plain Newton-min algorithm for linear complementarity problems with a P -matrix, Mathematical Programming, vol.134, pp.349-364, 2012. ,
URL : https://hal.archives-ouvertes.fr/inria-00442293
,
An algorithmic characterization of P-matricity, SIAM Journal on Matrix Analysis and Applications, vol.34, issue.3, pp.904-916, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00713330
An algorithmic characterization of P-matricity II: adjustments, refinements, and validation, SIAM Journal on Matrix Analysis and Applications, vol.40, issue.2, pp.800-813, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-01672197
Gas phase appearance and disappearance as a problem with complementarity constraints, Math. Comput. Simulation, vol.99, pp.28-36, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00641621
Numerical optimization, second edn, 2006. ,
Two-phase, partially miscible flow and transport modeling in porous media; application to gas migration in a nuclear waste repository, Comput. Geosci, vol.13, issue.5, pp.29-42, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00965384
Equilibrated residual error estimator for edge elements, Math. Comp, vol.77, issue.262, pp.651-672, 2008. ,
Mixed and hybrid finite element methods, Springer Series in Computational Mathematics, vol.15, 1991. ,
An a posteriori error estimate for vertex-centered finite volume discretizations of immiscible incompressible two-phase flow, Math. Comp, vol.83, issue.285, pp.153-188, 2014. ,
Mathematical models and finite elements for reservoir simulation, 1986. ,
Degenerate two-phase incompressible flow. I. Existence, uniqueness and regularity of a weak solution, J. Differential Equations, vol.171, issue.2, pp.203-232, 2001. ,
Reservoir simulation, CBMS-NSF Regional Conference Series in Applied Mathematics, vol.77, 2007. ,
Computational methods for multiphase flows in porous media, Society for Industrial and Applied Mathematics (SIAM), vol.2, 2006. ,
Residual type a posteriori error estimates for elliptic obstacle problems, Numer. Math, vol.84, issue.4, pp.527-548, 2000. ,
A Godunov-type finite volume method for the system of shallow water equations, Symposium on Advances in Computational Mechanics, vol.151, issue.1-2, pp.105-129, 1997. ,
Optimization and nonsmooth analysis, Society for Industrial and Applied Mathematics, vol.5, 1990. ,
Numerical simulation of non-isothermal multiphase multi-component processes in porous media. 1. An efficient solution technique, Adv. Water. Resour, pp.533-550, 2002. ,
Adaptive inexact semismooth Newton methods for the contact problem between two membranes, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01666845
Inexact Newton methods, SIAM J. Numer. Anal, vol.19, issue.2, pp.400-408, 1982. ,
Explicit error bounds in a conforming finite element method, Math. Comp, vol.68, issue.228, pp.1379-1396, 1999. ,
A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media, J. Comput. Phys, vol.276, pp.163-187, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00839487
An a posteriori-based, fully adaptive algorithm with adaptive stopping criteria and mesh refinement for thermal multiphase compositional flows in porous media, Comput. Math. Appl, vol.68, pp.2331-2347, 2014. ,
Globally convergent inexact Newton methods, SIAM J. Optim, vol.4, issue.2, pp.393-422, 1994. ,
Adaptive inexact Newton methods with a posteriori stopping criteria for nonlinear diffusion PDEs, SIAM J. Sci. Comput, vol.35, issue.4, pp.1761-1791, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00681422
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, pp.1058-1081, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-00921583
Finite volume methods, Handb. Numer. Anal., VII. North-Holland, 2000. ,
URL : https://hal.archives-ouvertes.fr/hal-02100732
Mathematical study of a petroleum-engineering scheme, M2AN Math. Model. Numer. Anal, vol.37, issue.6, pp.937-972, 2003. ,
A nonsmooth inexact Newton method for the solution of large-scale nonlinear complementarity problems, Math. Programming, vol.76, pp.493-512, 1997. ,
, Finite-dimensional variational inequalities and complementarity problems, 2003.
, Finite-dimensional variational inequalities and complementarity problems, 2003.
Numerical modeling of steam injection for the removal of nonaqeous phase liquids from the subsurface, Water. Resour. Res, vol.28, issue.1, pp.433-449, 1992. ,
A smoothing inexact Newton method for variational inequalities with nonlinear constraints, J. Inequal. Appl. pp. Paper No, vol.160, p.12, 2017. ,
Numerical methods for two-phase incompressible flows, Springer Series in Computational Mathematics, vol.40, 2011. ,
Multiphase flow and transport processes in the subsurface-A contribution to the modeling of hydrosystems, 1997. ,
Node-centered finite volume discretizations for the numerical simulation of multiphase flow in heterogeneous porous media, Comput. Geosci, vol.4, issue.2, pp.141-164, 2000. ,
A posteriori error estimates including algebraic error and stopping criteria for iterative solvers, SIAM J. Sci. Comput, vol.32, issue.3, pp.1567-1590, 2010. ,
Inexact semismooth Newton methods for large-scale complementarity problems, The First International Conference on Optimization Methods and Software. Part II, vol.19, pp.309-325, 2004. ,
A posteriori error estimates for a discontinuous Galerkin approximation of second-order elliptic problems, SIAM J. Numer. Anal, vol.41, issue.6, pp.2374-2399, 2003. ,
Iterative methods for linear and nonlinear equations, Society for Industrial and Applied Mathematics, vol.16, 1995. ,
A posteriori error estimates for elliptic variational inequalities, Comput. Math. Appl, vol.31, issue.8, pp.49-60, 1996. ,
Flow of oil and water in a porous medium, J. Differential Equations, vol.55, issue.2, pp.90084-90090, 1984. ,
Iterative solution methods for modeling multiphase flow in porous media fully implicitly, SIAM J. Sci. Comput, vol.25, issue.3, pp.905-926, 2003. ,
Comparaison de modèles de mécanique des milieux continus, 1975. ,
A new approach for phase transitions in miscible multi-phase flow in porous media, Advances in Water Resources, vol.68, pp.957-966, 2011. ,
Inexact Newton methods for solving nonsmooth equations, J. Comput. Appl. Math, vol.60, issue.1-2, pp.127-145, 1993. ,
Goal-oriented error control of the iterative solution of finite element equations, J. Numer. Math, vol.17, issue.2, pp.143-172, 2009. ,
Multi-scale modeling of three-phase-three-component processes in heterogeneous porous media, Advances in Water Resources, vol.30, pp.2309-2325, 2007. ,
Method of negative saturations for flow with variable number of phases in porous media: extension to three-phase multi-component case, Comput. Geosci, vol.18, issue.5, pp.385-399, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01418288
Interfaces of phase transition and disappearance and method of negative saturation for compositional flow with diffusion and capillarity in porous media, Transp. Porous. Med, vol.83, issue.5, pp.73-98, 2010. ,
Sharp algebraic and total a posteriori error bounds for h and p finite elements via a multilevel approach, 2017. ,
An optimal Poincaré inequality for convex domains, Arch. Rational Mech. Anal, vol.5, pp.286-292, 1960. ,
Mixed finite elements for the Richards' equation: linearization procedure, J. Comput. Appl. Math, vol.168, issue.1-2, pp.365-373, 2004. ,
Approximations in elasticity based on the concept of function space, Quart. Appl. Math, vol.5, pp.241-269, 1947. ,
A robust, mass conservative scheme for two-phase flow in porous media including Hölder continuous nonlinearities, IMA J. Numer. Anal, vol.38, issue.2, pp.884-920, 2018. ,
A mixed finite element method for 2nd order elliptic problems pp, Lecture Notes in Math, vol.606, pp.292-315, 1977. ,
A posteriori estimates for partial differential equations, Radon Series on Computational and Applied Mathematics, vol.4, 2008. ,
Functional a posteriori estimates for elliptic variational inequalities, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), vol.348, p.305, 2007. ,
Mixed and hybrid methods, Handbook of Numerical Analysis, vol.II, pp.523-639, 1991. ,
URL : https://hal.archives-ouvertes.fr/inria-00075815
Henry' law and gas phase disappearance, Transport in porous media, vol.82, pp.521-526, 2010. ,
URL : https://hal.archives-ouvertes.fr/inria-00374073
Novel porous media formulation for multiphase flow conservation equations, 2011. ,
A robust and efficient linearization scheme for doubly nonlinear and degenerate parabolic problems arising in flow in porous media, SIAM J. Sci. Comput, vol.23, issue.5, pp.1593-1614, 2002. ,
Efficient and reliable a posteriori error estimators for elliptic obstacle problems, SIAM J. Numer. Anal, vol.39, issue.1, pp.146-167, 2001. ,
Residual flux-based a posteriori error estimates for finite volume and related locally conservative methods, Numer. Math, vol.111, issue.1, pp.121-158, 2008. ,
A posteriori error estimates, stopping criteria, and adaptivity for twophase flows, Comput. Geosci, vol.17, issue.5, pp.789-812, 2013. ,