EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues ESAIM: M2AN, 37 6 (2003) 937-972 Article references

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:

Convergence of a TPFA finite volume scheme for nonisothermal immiscible compressible two-phase flow in porous media

Brahim Amaziane, Mustapha El Ossmani and Youssef Zahraoui
Computers & Mathematics with Applications 165 118 (2024)
https://doi.org/10.1016/j.camwa.2024.04.010

Thermodynamically consistent numerical modeling of immiscible two‐phase flow in poro‐viscoelastic media

Jisheng Kou, Amgad Salama, Huangxin Chen and Shuyu Sun
International Journal for Numerical Methods in Engineering 125 (14) (2024)
https://doi.org/10.1002/nme.7479

Computational modeling of early-stage breast cancer progression using TPFA method: A numerical investigation

Manal Alotaibi, Françoise Foucher, Moustafa Ibrahim and Mazen Saad
Applied Numerical Mathematics 198 236 (2024)
https://doi.org/10.1016/j.apnum.2024.01.010

Discretization schemes for the two simplified global double porosity models of immiscible incompressible two-phase flow

M Jurak, L Pankratov and A Vrbaški
Journal of Physics: Conference Series 2701 (1) 012077 (2024)
https://doi.org/10.1088/1742-6596/2701/1/012077

Discrete energy balance equation via a symplectic second-order method for two-phase flow in porous media

Giselle Sosa Jones and Catalin Trenchea
Applied Mathematics and Computation 480 128909 (2024)
https://doi.org/10.1016/j.amc.2024.128909

An energy stable and positivity-preserving computational method for compressible and immiscible two-phase flow in porous media

Jisheng Kou, Huangxin Chen, Amgad Salama and Shuyu Sun
Journal of Computational Physics 519 113391 (2024)
https://doi.org/10.1016/j.jcp.2024.113391

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 43 (5) 2714 (2023)
https://doi.org/10.1093/imanum/drac053

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)
https://doi.org/10.1002/nme.7222

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)
https://doi.org/10.1016/j.cam.2021.113728

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

Clément Cancès and Antoine Zurek
Numerische Mathematik 151 (1) 279 (2022)
https://doi.org/10.1007/s00211-022-01270-7

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)
https://doi.org/10.1093/imanum/draa064

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)
https://doi.org/10.1093/imanum/drab018

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)
https://doi.org/10.1007/s10444-022-09972-0

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)
https://doi.org/10.1016/j.cma.2021.114550

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)
https://doi.org/10.1051/m2an/2022050

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)
https://doi.org/10.1051/m2an/2021047

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)
https://doi.org/10.1051/m2an/2021063

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)
https://doi.org/10.1515/jnma-2020-0005

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)
https://doi.org/10.1137/19M1284233

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)
https://doi.org/10.1515/jnma-2020-0004

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)
https://doi.org/10.1137/19M1260165

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)
https://doi.org/10.1007/978-3-030-43651-3_18

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)
https://doi.org/10.1007/s10596-019-09909-5

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)
https://doi.org/10.1002/num.22422

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)
https://doi.org/10.1016/j.jcp.2020.109233

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)
https://doi.org/10.1016/j.cam.2018.12.022

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)
https://doi.org/10.1137/17M1160744

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)
https://doi.org/10.1017/S0956792518000633

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)
https://doi.org/10.1007/s00205-019-01369-6

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)
https://doi.org/10.1007/s10596-018-9794-9

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)
https://doi.org/10.1007/s10596-018-9783-z

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)
https://doi.org/10.1016/j.apnum.2019.07.009

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)
https://doi.org/10.1093/imanum/drx078

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)
https://doi.org/10.1002/num.22234

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)
https://doi.org/10.1016/j.camwa.2018.04.037

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)
https://doi.org/10.1016/j.camwa.2018.02.021

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)
https://doi.org/10.1093/imanum/drx032

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)
https://doi.org/10.1016/j.cam.2017.12.037

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)
https://doi.org/10.2516/ogst/2018067

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)
https://doi.org/10.1007/s00211-016-0839-5

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)
https://doi.org/10.1007/978-3-319-63082-3_104

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)
https://doi.org/10.1016/j.advwatres.2017.07.028

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)
https://doi.org/10.1007/978-3-319-57397-7_36

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)
https://doi.org/10.1016/j.camwa.2015.12.010

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)
https://doi.org/10.1016/j.cma.2016.08.009

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

Jérôme Droniou and Robert Eymard
Numerische Mathematik 132 (4) 721 (2016)
https://doi.org/10.1007/s00211-015-0733-6

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)
https://doi.org/10.1137/15M1020988

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)
https://doi.org/10.1007/s00211-014-0651-z

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)
https://doi.org/10.1007/s10596-014-9455-6

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)
https://doi.org/10.1051/m2an/2014034

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)
https://doi.org/10.1016/j.camwa.2014.08.008

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)
https://doi.org/10.1002/num.21823

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)
https://doi.org/10.1002/zamm.201200206

Derivation of Seawater Intrusion Models by Formal Asymptotics

M. Jazar and R. Monneau
SIAM Journal on Applied Mathematics 74 (4) 1152 (2014)
https://doi.org/10.1137/120867561

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)
https://doi.org/10.3934/dcdss.2014.7.317

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)
https://doi.org/10.1016/j.jcp.2014.06.061

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)
https://doi.org/10.1142/S0218202513500498

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)
https://doi.org/10.1007/s10596-014-9403-5

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)
https://doi.org/10.1007/s10596-013-9345-3

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)
https://doi.org/10.1002/num.21715

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)
https://doi.org/10.1137/120869092

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)
https://doi.org/10.1142/S0218202512500613

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

Martin Vohralík and Mary F. Wheeler
Computational Geosciences 17 (5) 789 (2013)
https://doi.org/10.1007/s10596-013-9356-0

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)
https://doi.org/10.1016/j.na.2010.03.040

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

Alexandre Ern, Igor Mozolevski and L. Schuh
Comptes Rendus. Mathématique 347 (9-10) 551 (2009)
https://doi.org/10.1016/j.crma.2009.02.011

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)
https://doi.org/10.1016/j.cam.2008.08.026

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)
https://doi.org/10.1016/j.jmaa.2006.02.082