A reduced fracture model for two-phase flow with different rock types, Mathematics and Computers in Simulation, vol.137, pp.49-70, 2017. ,
DOI : 10.1016/j.matcom.2016.10.005
URL : https://hal.archives-ouvertes.fr/hal-01249322
A finite volume Schwarz algorithm for two-phase immiscible flow with different rock types ,
A posteriori error estimates and stopping criteria for solvers using domain decomposition method and with local time stepping, 2017. ,
A posteriori stopping criteria for optimized Schwarz domain decomposition algorithms in mixed formulations. HAL Preprint 01529532, submitted for publication, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01529532
Approximating the vanishing capillarity limit of two-phase flow in multi-dimensional heterogeneous porous medium, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f?r Angewandte Mathematik und Mechanik, vol.38, issue.2, pp.655-667, 2014. ,
DOI : 10.1002/zamm.201200218
URL : https://hal.archives-ouvertes.fr/hal-00744359
Stopping criteria for iterations in finite element methods, Numerische Mathematik, vol.15, issue.3, pp.381-410, 2005. ,
DOI : 10.1145/321406.321416
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.6.5563
Petroleum Reservoir Simulation, Applied Science Publishers, 1979. ,
A homographic best approximation problem with application to optimized Schwarz waveform relaxation, Mathematics of Computation, vol.78, issue.265, pp.185-223, 2009. ,
DOI : 10.1090/S0025-5718-08-02145-5
URL : https://hal.archives-ouvertes.fr/hal-00111643
The 2-Lagrange Multiplier Method Applied to Nonlinear Transmission Problems for the Richards Equation in Heterogeneous Soil with Cross Points, SIAM Journal on Scientific Computing, vol.36, issue.5, pp.2166-2198, 2014. ,
DOI : 10.1137/120901064
Substructuring of a Signorini-type problem and Robin?s method for the Richards equation in heterogeneous soil, Computing and Visualization in Science, vol.44, issue.2, pp.187-205, 2010. ,
DOI : 10.1007/s00791-010-0141-5
Finite volume approximation for an immiscible two-phase flow in porous media with discontinuous capillary pressure, Computational Geosciences, vol.21, issue.4, pp.573-597, 2013. ,
DOI : 10.1007/s10596-013-9345-3
URL : https://hal.archives-ouvertes.fr/hal-00675681
Schwarz waveform relaxation algorithms for semilinear reaction-diffusion equations, Netw. Heterog. Media, pp.487-505, 2010. ,
DOI : 10.3934/nhm.2010.5.487
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.297.4450
Nonlinear Parabolic Equations with Spatial Discontinuities, Nonlinear Differential Equations and Applications NoDEA, vol.15, issue.4-5, pp.427-456, 2008. ,
DOI : 10.1007/s00030-008-6030-7
Two-phase flows involving capillary barriers in heterogeneous porous media, Interfaces Free Bound, pp.239-258, 2009. ,
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
Mathematical models and finite elements for reservoir simulation, North- Holland, Studies in Mathematics and Its Applications, 1986. ,
A posteriori error estimates of mixed methods for miscible displacement problems, International Journal for Numerical Methods in Engineering, vol.93, issue.3, pp.331-343, 2008. ,
DOI : 10.1007/978-1-4612-3172-1
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
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
Adaptive regularization, linearization, and discretization and a posteriori error control for the two-phase Stefan problem, Mathematics of Computation, vol.84, issue.291, pp.153-186, 2015. ,
DOI : 10.1090/S0025-5718-2014-02854-8
URL : https://hal.archives-ouvertes.fr/hal-00690862
Numerical Approximation of a Two-phase Flow Problem in a Porous Medium with Discontinuous Capillary Forces, SIAM Journal on Numerical Analysis, vol.43, issue.6, pp.2402-2422, 2006. ,
DOI : 10.1137/040602936
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
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
Finite volume methods, in Handbook of Numerical Analysis, pp.713-1020, 2000. ,
Finite volume approximation of elliptic problems and convergence of an approximate gradient, Applied Numerical Mathematics, vol.37, issue.1-2, pp.31-53, 2001. ,
DOI : 10.1016/S0168-9274(00)00024-6
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
A Global Jacobian Method for Mortar Discretizations of a Fully Implicit Two-Phase Flow Model, Multiscale Modeling & Simulation, vol.12, issue.4, pp.1401-1423, 2014. ,
DOI : 10.1137/140952922
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
A Finite Volume Ventcell-Schwarz Algorithm for Advection-Diffusion Equations, SIAM Journal on Numerical Analysis, vol.52, issue.3, pp.1269-1291, 2014. ,
DOI : 10.1137/130919799
URL : https://hal.archives-ouvertes.fr/hal-01271249
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
Ventcell Conditions with Mixed Formulations for Flow in Porous Media, Lecture Notes in Computational Science and Engineering, vol.104, pp.531-540, 2016. ,
DOI : 10.1007/978-3-319-18827-0_54
URL : https://hal.archives-ouvertes.fr/hal-01113964
The best interface conditions for domain decomposition methods: absorbing boundary conditions, in Absorbing Boundaries and Layers, Domain Decomposition Methods, pp.348-373, 2001. ,
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
A posteriori error estimators for locally conservative methods of nonlinear elliptic problems, Applied Numerical Mathematics, vol.57, issue.9, pp.1065-1080, 2007. ,
DOI : 10.1016/j.apnum.2006.09.010
Open-source MATLAB implementation of consistent discretisations on complex grids, Computational Geosciences, vol.13, issue.2, pp.297-322, 2012. ,
DOI : 10.1007/s10596-011-9244-4
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
A posteriori error estimation and adaptivity for degenerate parabolic
problems, Mathematics of Computation, vol.69, issue.229, pp.1-24, 2000. ,
DOI : 10.1090/S0025-5718-99-01097-2
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.105.8965
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
Analysis and Upscaling of a Reactive Transport Model in Fractured Porous Media with Nonlinear Transmission Condition, Vietnam Journal of Mathematics, vol.219, issue.1-2, pp.77-102, 2017. ,
DOI : 10.1007/s11242-015-0547-0
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 : 10.1002/nme.5244
URL : https://hal.archives-ouvertes.fr/hal-01332674
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
Domain decomposition strategies for nonlinear flow problems in porous media, Journal of Computational Physics, vol.234, pp.439-451, 2013. ,
DOI : 10.1016/j.jcp.2012.10.001
Two-scale preconditioning for twophase nonlinear flows in porous media, Transp. Porous Media, pp.485-503, 2016. ,
The effect of capillary forces on immiscible two-phase flow in heterogeneous porous media, Transport in Porous Media, pp.71-93, 1995. ,
A posteriori error estimates for finite element discretizations of the heat equation, pp.40-195, 2003. ,
Unified primal formulation-based a priori and a posteriori error analysis of mixed finite element methods, Mathematics of Computation, vol.79, issue.272, 2001. ,
DOI : 10.1090/S0025-5718-2010-02375-0
A posteriori error estimates, stopping criteria, and adaptivity for two-phase flows, Computational Geosciences, vol.17, issue.5, pp.789-812, 2013. ,
DOI : 10.1007/s10596-013-9356-0
A mixed finite element discretization on non-matching multiblock grids for a degenerate parabolic equation arising in porous media flow, East-West J. Numer. Math, vol.5, pp.211-230, 1997. ,
Interface solvers and preconditioners of domain decomposition type for multiphase flow in multiblock porous media, Scientific computing and applications, pp.157-167, 2001. ,