Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

This article has been cited by the following article(s):

The Gradient Discretization Method for Slow and Fast Diffusion Porous Media Equations

Jérôme Droniou and Kim-Ngan Le
SIAM Journal on Numerical Analysis 58 (3) 1965 (2020)
DOI: 10.1137/19M1260165
See this article

Gradient schemes for two-phase flow in heterogeneous porous media and Richards equation

R. Eymard, C. Guichard, R. Herbin and R. Masson
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 94 (7-8) 560 (2014)
DOI: 10.1002/zamm.201200206
See this article

Numerical analysis of a non equilibrium two-component two-compressible flow in porous media

Bilal Saad and Mazen Saad
Discrete & Continuous Dynamical Systems - S 7 (2) 317 (2014)
DOI: 10.3934/dcdss.2014.7.317
See this article

Finite volume approximation for an immiscible two-phase flow in porous media with discontinuous capillary pressure

Konstantin Brenner, Clément Cancès and Danielle Hilhorst
Computational Geosciences 17 (3) 573 (2013)
DOI: 10.1007/s10596-013-9345-3
See this article

Convergence of a finite volume scheme for immiscible compressible two-phase flow in porous media by the concept of the global pressure

Brahim Amaziane, Mladen Jurak and Ivana Radišić
Journal of Computational and Applied Mathematics 399 113728 (2022)
DOI: 10.1016/j.cam.2021.113728
See this article

G. Enchery, M. Le Ravalec-Dupin and F. Roggero
(2007)
DOI: 10.2118/107088-MS
See this article

A Two-Phase Two-Fluxes Degenerate Cahn–Hilliard Model as Constrained Wasserstein Gradient Flow

Clément Cancès, Daniel Matthes and Flore Nabet
Archive for Rational Mechanics and Analysis 233 (2) 837 (2019)
DOI: 10.1007/s00205-019-01369-6
See this article

Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects

Clément Cancès and Flore Nabet
Springer Proceedings in Mathematics & Statistics, Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects 199 431 (2017)
DOI: 10.1007/978-3-319-57397-7_36
See this article

MIXED FINITE ELEMENT METHODS: IMPLEMENTATION WITH ONE UNKNOWN PER ELEMENT, LOCAL FLUX EXPRESSIONS, POSITIVITY, POLYGONAL MESHES, AND RELATIONS TO OTHER METHODS

MARTIN VOHRALÍK and BARBARA I. WOHLMUTH
Mathematical Models and Methods in Applied Sciences 23 (05) 803 (2013)
DOI: 10.1142/S0218202512500613
See this article

Total velocity-based finite volume discretization of two-phase Darcy flow in highly heterogeneous media with discontinuous capillary pressure

K Brenner, R Masson, E H Quenjel and J Droniou
IMA Journal of Numerical Analysis 42 (2) 1231 (2022)
DOI: 10.1093/imanum/drab018
See this article

Numerical analysis of a finite volume scheme for a seawater intrusion model with cross-diffusion in an unconfined aquifer

Ahmed Ait Hammou Oulhaj
Numerical Methods for Partial Differential Equations 34 (3) 857 (2018)
DOI: 10.1002/num.22234
See this article

Numerical analysis for two-phase flow with non-equilibrium capillary pressure in anisotropic porous media

Khaled Bouadjila, Ali Samir Saad, Mazen Saad and Wissal Mesfar
Advances in Computational Mathematics 48 (5) (2022)
DOI: 10.1007/s10444-022-09972-0
See this article

Three Models for Two Phase Flow in Porous Media

Nils Henrik Risebro
Vietnam Journal of Mathematics 47 (4) 835 (2019)
DOI: 10.1007/s10013-019-00367-1
See this article

Implicit Hybrid Upwind scheme for coupled multiphase flow and transport with buoyancy

François P. Hamon, Bradley T. Mallison and Hamdi A. Tchelepi
Computer Methods in Applied Mechanics and Engineering 311 599 (2016)
DOI: 10.1016/j.cma.2016.08.009
See this article

Convergence of an MPFA finite volume scheme for a two‐phase porous media flow model with dynamic capillarity

X Cao, S F Nemadjieu and I S Pop
IMA Journal of Numerical Analysis (2018)
DOI: 10.1093/imanum/drx078
See this article

Accurate velocity reconstruction for Discontinuous Galerkin approximations of two-phase porous media flows

Alexandre Ern, Igor Mozolevski and L. Schuh
Comptes Rendus Mathematique 347 (9-10) 551 (2009)
DOI: 10.1016/j.crma.2009.02.011
See this article

Maximum-principle-satisfying discontinuous Galerkin methods for incompressible two-phase immiscible flow

M.S. Joshaghani, B. Riviere and M. Sekachev
Computer Methods in Applied Mechanics and Engineering 391 114550 (2022)
DOI: 10.1016/j.cma.2021.114550
See this article

Study of a numerical scheme for miscible two-phase flow in porous media

Robert Eymard and Veronika Schleper
Numerical Methods for Partial Differential Equations 30 (3) 723 (2014)
DOI: 10.1002/num.21823
See this article

Vertex Approximate Gradient Scheme for Hybrid Dimensional Two-Phase Darcy Flows in Fractured Porous Media

K. Brenner, M. Groza, C. Guichard and R. Masson
ESAIM: Mathematical Modelling and Numerical Analysis 49 (2) 303 (2015)
DOI: 10.1051/m2an/2014034
See this article

Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples

Clément Cancès and Flore Nabet
Springer Proceedings in Mathematics & Statistics, Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples 323 213 (2020)
DOI: 10.1007/978-3-030-43651-3_18
See this article

An a posteriori-based, fully adaptive algorithm with adaptive stopping criteria and mesh refinement for thermal multiphase compositional flows in porous media

Daniele A. Di Pietro, Martin Vohralík and Soleiman Yousef
Computers & Mathematics with Applications 68 (12) 2331 (2014)
DOI: 10.1016/j.camwa.2014.08.008
See this article

A combined finite volume–nonconforming finite element scheme for compressible two phase flow in porous media

Bilal Saad and Mazen Saad
Numerische Mathematik 129 (4) 691 (2015)
DOI: 10.1007/s00211-014-0651-z
See this article

Adaptive heterogeneous multiscale methods for immiscible two-phase flow in porous media

Patrick Henning, Mario Ohlberger and Ben Schweizer
Computational Geosciences 19 (1) 99 (2015)
DOI: 10.1007/s10596-014-9455-6
See this article

Study of Full Implicit Petroleum Engineering Finite-Volume Scheme for Compressible Two-Phase Flow in Porous Media

Bilal Saad and Mazen Saad
SIAM Journal on Numerical Analysis 51 (1) 716 (2013)
DOI: 10.1137/120869092
See this article

Simulation of multiphase porous media flows with minimising movement and finite volume schemes

CLÉMENT CANCÈS, THOMAS GALLOUËT, MAXIME LABORDE and LÉONARD MONSAINGEON
European Journal of Applied Mathematics 30 (6) 1123 (2019)
DOI: 10.1017/S0956792518000633
See this article

On nonlinear diffusion problems with strong degeneracy

Kaouther Ammar
Journal of Differential Equations 244 (8) 1841 (2008)
DOI: 10.1016/j.jde.2007.11.013
See this article

On the convergence analysis of a hybrid numerical method for multicomponent transport in porous media

Prabir Daripa and Sourav Dutta
Applied Numerical Mathematics 146 199 (2019)
DOI: 10.1016/j.apnum.2019.07.009
See this article

Existence of a solution for two phase flow in porous media: The case that the porosity depends on the pressure

F.Z. Daïm, R. Eymard and D. Hilhorst
Journal of Mathematical Analysis and Applications 326 (1) 332 (2007)
DOI: 10.1016/j.jmaa.2006.02.082
See this article

Boiling in Porous Media: Model and Simulations

Johann B�nard, Robert Eymard, Xavier Nicolas and Cl�ment Chavant
Transport in Porous Media 60 (1) 1 (2005)
DOI: 10.1007/s11242-004-2594-9
See this article

Upstream mobility finite volumes for the Richards equation in heterogenous domains

Sabrina Bassetto, Clément Cancès, Guillaume Enchéry and Quang-Huy Tran
ESAIM: Mathematical Modelling and Numerical Analysis 55 (5) 2101 (2021)
DOI: 10.1051/m2an/2021047
See this article

CONVERGENCE OF A FINITE VOLUME SCHEME FOR GAS–WATER FLOW IN A MULTI-DIMENSIONAL POROUS MEDIUM

MOSTAFA BENDAHMANE, ZIAD KHALIL and MAZEN SAAD
Mathematical Models and Methods in Applied Sciences 24 (01) 145 (2014)
DOI: 10.1142/S0218202513500498
See this article

A finite element method for degenerate two-phase flow in porous media. Part I: Well-posedness

Vivette Girault, Beatrice Riviere and Loic Cappanera
Journal of Numerical Mathematics 29 (2) 81 (2021)
DOI: 10.1515/jnma-2020-0004
See this article

Progress in Industrial Mathematics at ECMI 2016

Houssein Nasser El Dine, Mazen Saad and Raafat Talhouk
Mathematics in Industry, Progress in Industrial Mathematics at ECMI 2016 26 695 (2017)
DOI: 10.1007/978-3-319-63082-3_104
See this article

Convergence of a positive nonlinear Control Volume Finite Element scheme for solving an anisotropic degenerate breast cancer development model

Françoise Foucher, Moustafa Ibrahim and Mazen Saad
Computers & Mathematics with Applications 76 (3) 551 (2018)
DOI: 10.1016/j.camwa.2018.04.037
See this article

TP or not TP, that is the question

R. Eymard, T. Gallouët, C. Guichard, R. Herbin and R. Masson
Computational Geosciences 18 (3-4) 285 (2014)
DOI: 10.1007/s10596-013-9392-9
See this article

Error estimates for a mixed finite element discretization of a two-phase porous media flow model with dynamic capillarity

Xiulei Cao and Koondanibha Mitra
Journal of Computational and Applied Mathematics 353 164 (2019)
DOI: 10.1016/j.cam.2018.12.022
See this article

Finite volume approximation of degenerate two-phase flow model with unlimited air mobility

Boris Andreianov, Robert Eymard, Mustapha Ghilani and Nouzha Marhraoui
Numerical Methods for Partial Differential Equations 29 (2) 441 (2013)
DOI: 10.1002/num.21715
See this article

A robust, mass conservative scheme for two-phase flow in porous media including Hölder continuous nonlinearities

Florin A Radu, Kundan Kumar, Jan M Nordbotten and Iuliu S Pop
IMA Journal of Numerical Analysis 38 (2) 884 (2018)
DOI: 10.1093/imanum/drx032
See this article

Derivation of Seawater Intrusion Models by Formal Asymptotics

M. Jazar and R. Monneau
SIAM Journal on Applied Mathematics 74 (4) 1152 (2014)
DOI: 10.1137/120867561
See this article

Analysis of a finite volume–finite element method for Darcy–Brinkman two-phase flows in porous media

Houssein Nasser El Dine and Mazen Saad
Journal of Computational and Applied Mathematics 337 51 (2018)
DOI: 10.1016/j.cam.2017.12.037
See this article

Degenerate triply nonlinear problems with nonhomogeneous boundary conditions

Kaouther Ammar
Central European Journal of Mathematics 8 (3) 548 (2010)
DOI: 10.2478/s11533-010-0032-5
See this article

A nonnegativity preserving scheme for the relaxed Cahn–Hilliard equation with single-well potential and degenerate mobility

Federica Bubba and Alexandre Poulain
ESAIM: Mathematical Modelling and Numerical Analysis 56 (5) 1741 (2022)
DOI: 10.1051/m2an/2022050
See this article

A posteriori error estimates for a compositional two-phase flow with nonlinear complementarity constraints

Ibtihel Ben Gharbia, Jad Dabaghi, Vincent Martin and Martin Vohralík
Computational Geosciences 24 (3) 1031 (2020)
DOI: 10.1007/s10596-019-09909-5
See this article

Two-phase flow equations with outflow boundary conditions in the hydrophobic–hydrophilic case

Michael Lenzinger and Ben Schweizer
Nonlinear Analysis: Theory, Methods & Applications 73 (4) 840 (2010)
DOI: 10.1016/j.na.2010.03.040
See this article

Numerical study of compositional compressible degenerate two-phase flow in saturated–unsaturated heterogeneous porous media

Ali S. Saad, Bilal Saad and Mazen Saad
Computers & Mathematics with Applications 71 (2) 565 (2016)
DOI: 10.1016/j.camwa.2015.12.010
See this article

Polyhedral Methods in Geosciences

Clément Cancès, Jérôme Droniou, Cindy Guichard, et al.
SEMA SIMAI Springer Series, Polyhedral Methods in Geosciences 27 37 (2021)
DOI: 10.1007/978-3-030-69363-3_2
See this article

A phase-by-phase upstream scheme that converges to the vanishing capillarity solution for countercurrent two-phase flow in two-rock media

Boris Andreianov and Clément Cancès
Computational Geosciences 18 (2) 211 (2014)
DOI: 10.1007/s10596-014-9403-5
See this article

Analysis of an interior penalty discontinuous Galerkin scheme for two phase flow in porous media with dynamic capillary effects

Stefan Karpinski and Iuliu Sorin Pop
Numerische Mathematik 136 (1) 249 (2017)
DOI: 10.1007/s00211-016-0839-5
See this article

Positive control volume finite element scheme for a degenerate compressible two-phase flow in anisotropic porous media

Mustapha Ghilani, EL Houssaine Quenjel and Mazen Saad
Computational Geosciences 23 (1) 55 (2019)
DOI: 10.1007/s10596-018-9783-z
See this article

Uniform-in-time convergence of numerical methods for non-linear degenerate parabolic equations

Jérôme Droniou and Robert Eymard
Numerische Mathematik 132 (4) 721 (2016)
DOI: 10.1007/s00211-015-0733-6
See this article

A vertex scheme for two-phase flow in heterogeneous media

M.S. Joshaghani, V. Girault and B. Riviere
Journal of Computational Physics 449 110778 (2022)
DOI: 10.1016/j.jcp.2021.110778
See this article

A posteriori error estimates, stopping criteria, and adaptivity for two-phase flows

Martin Vohralík and Mary F. Wheeler
Computational Geosciences 17 (5) 789 (2013)
DOI: 10.1007/s10596-013-9356-0
See this article

Efficient C1-continuous phase-potential upwind (C1-PPU) schemes for coupled multiphase flow and transport with gravity

Jiamin Jiang and Rami M. Younis
Advances in Water Resources 108 184 (2017)
DOI: 10.1016/j.advwatres.2017.07.028
See this article

Analysis of Hybrid Upwinding for Fully-Implicit Simulation of Three-Phase Flow with Gravity

François P. Hamon and Hamdi A. Tchelepi
SIAM Journal on Numerical Analysis 54 (3) 1682 (2016)
DOI: 10.1137/15M1020988
See this article

Non-isothermal compositional liquid gas Darcy flow: formulation, soil-atmosphere boundary condition and application to high-energy geothermal simulations

Laurence Beaude, Konstantin Brenner, Simon Lopez, Roland Masson and Farid Smai
Computational Geosciences 23 (3) 443 (2019)
DOI: 10.1007/s10596-018-9794-9
See this article

Energy stable numerical methods for porous media flow type problems

Clément Cancès, A. Anciaux-Sedrakian and Q. H. Tran
Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles 73 78 (2018)
DOI: 10.2516/ogst/2018067
See this article

Control Volume Approximation of Degenerate Two-Phase Porous Flows

Thomas J. Murphy and Noel J. Walkington
SIAM Journal on Numerical Analysis 57 (2) 527 (2019)
DOI: 10.1137/17M1160744
See this article

Convergence of a positive nonlinear control volume finite element scheme for an anisotropic seawater intrusion model with sharp interfaces

Ahmed Ait Hammou Oulhaj and David Maltese
Numerical Methods for Partial Differential Equations 36 (1) 133 (2020)
DOI: 10.1002/num.22422
See this article

Numerical analysis of a finite volume scheme for two incompressible phase flow with dynamic capillary pressure

Khaled Bouadjila, Abdelhafid Mokrane, Ali Samir Saad and Mazen Saad
Computers & Mathematics with Applications 75 (10) 3614 (2018)
DOI: 10.1016/j.camwa.2018.02.021
See this article

A Gravity Current Model with Capillary Trapping for Oil Migration in Multilayer Geological Basins

Clément Cancès and David Maltese
SIAM Journal on Applied Mathematics 81 (2) 454 (2021)
DOI: 10.1137/19M1284233
See this article

A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media

Daniele A. Di Pietro, Eric Flauraud, Martin Vohralík and Soleiman Yousef
Journal of Computational Physics 276 163 (2014)
DOI: 10.1016/j.jcp.2014.06.061
See this article

Positivity-preserving finite volume scheme for compressible two-phase flows in anisotropic porous media: The densities are depending on the physical pressures

Mustapha Ghilani, El Houssaine Quenjel and Mazen Saad
Journal of Computational Physics 407 109233 (2020)
DOI: 10.1016/j.jcp.2020.109233
See this article

A finite element method for degenerate two-phase flow in porous media. Part II: Convergence

Vivette Girault, Beatrice Riviere and Loic Cappanera
Journal of Numerical Mathematics 29 (3) 187 (2021)
DOI: 10.1515/jnma-2020-0005
See this article

Convergence of nonlinear finite volume schemes for two-phase porous media flow on general meshes

Léo Agélas, Martin Schneider, Guillaume Enchéry and Bernd Flemisch
IMA Journal of Numerical Analysis 42 (1) 515 (2022)
DOI: 10.1093/imanum/draa064
See this article

A convergent finite volume scheme for dissipation driven models with volume filling constraint

Clément Cancès and Antoine Zurek
Numerische Mathematik 151 (1) 279 (2022)
DOI: 10.1007/s00211-022-01270-7
See this article

An energy stable, conservative and bounds‐preserving numerical method for thermodynamically consistent modeling of incompressible two‐phase flow in porous media with rock compressibility

Jisheng Kou, Xiuhua Wang, Huangxin Chen and Shuyu Sun
International Journal for Numerical Methods in Engineering 124 (11) 2589 (2023)
DOI: 10.1002/nme.7222
See this article

Global existence of weak solutions to unsaturated poroelasticity

Jakub Wiktor Both, Iuliu Sorin Pop and Ivan Yotov
ESAIM: Mathematical Modelling and Numerical Analysis 55 (6) 2849 (2021)
DOI: 10.1051/m2an/2021063
See this article

Analysis of hp discontinuous Galerkin methods for incompressible two-phase flow

Yekaterina Epshteyn and Beatrice Rivière
Journal of Computational and Applied Mathematics 225 (2) 487 (2009)
DOI: 10.1016/j.cam.2008.08.026
See this article

Existence and convergence of a discontinuous Galerkin method for the incompressible three-phase flow problem in porous media

Giselle Sosa Jones, Loïc Cappanera and Beatrice Riviere
IMA Journal of Numerical Analysis (2022)
DOI: 10.1093/imanum/drac053
See this article