On fully practical finite element approximations of degenerate Cahn-Hilliard systems
ESAIM: M2AN, 35 4 (2001) 713-748
Published online: 2002-04-15
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):
(2024)
https://doi.org/10.2139/ssrn.4846682
A Local Continuum Model of Cell-Cell Adhesion
C. Falcó, R. E. Baker and J. A. CarrilloSIAM Journal on Applied Mathematics 84 (3) S17 (2024)
https://doi.org/10.1137/22M1506079
An explicit time integration method for Boussinesq approximation
Dandy Rueda Castillo, Utku Kaya and Thomas RichterPAMM 24 (4) (2024)
https://doi.org/10.1002/pamm.202400050
A second-order structure-preserving discretization for the Cahn-Hilliard/Allen-Cahn system with cross-kinetic coupling
Aaron Brunk, Herbert Egger and Oliver HabrichApplied Numerical Mathematics 206 12 (2024)
https://doi.org/10.1016/j.apnum.2024.07.016
A structure-preserving finite element method for the multi-phase Mullins–Sekerka problem with triple junctions
Tokuhiro Eto, Harald Garcke and Robert NürnbergNumerische Mathematik 156 (4) 1479 (2024)
https://doi.org/10.1007/s00211-024-01414-x
A uniqueness theory on determining the nonlinear energy potential in phase-field system
Tianhao Ni and Jun LaiInverse Problems 40 (12) 125005 (2024)
https://doi.org/10.1088/1361-6420/ad89f4
Stability and discretization error analysis for the Cahn–Hilliard system via relative energy estimates
Aaron Brunk, Herbert Egger, Oliver Habrich and Mária Lukáčová-MedviďováESAIM: Mathematical Modelling and Numerical Analysis 57 (3) 1297 (2023)
https://doi.org/10.1051/m2an/2023017
A convergent SAV scheme for Cahn–Hilliard equations with dynamic boundary conditions
Stefan MetzgerIMA Journal of Numerical Analysis 43 (6) 3593 (2023)
https://doi.org/10.1093/imanum/drac078
6 (2022)
https://doi.org/10.1117/12.2648662
Efficient and energy stable scheme for the hydrodynamically coupled three components Cahn-Hilliard phase-field model using the stabilized-Invariant Energy Quadratization (S-IEQ) Approach
Xiaofeng YangJournal of Computational Physics 438 110342 (2021)
https://doi.org/10.1016/j.jcp.2021.110342
In Silico Mathematical Modelling for Glioblastoma: A Critical Review and a Patient-Specific Case
Jacopo Falco, Abramo Agosti, Ignazio G. Vetrano, Alberto Bizzi, Francesco Restelli, Morgan Broggi, Marco Schiariti, Francesco DiMeco, Paolo Ferroli, Pasquale Ciarletta and Francesco AcerbiJournal of Clinical Medicine 10 (10) 2169 (2021)
https://doi.org/10.3390/jcm10102169
A stable FE method for the space-time solution of the Cahn-Hilliard equation
Eirik Valseth, Albert Romkes and Austin R. KaulJournal of Computational Physics 441 110426 (2021)
https://doi.org/10.1016/j.jcp.2021.110426
An Efficient and Convergent Finite Element Scheme for Cahn--Hilliard Equations with Dynamic Boundary Conditions
Stefan MetzgerSIAM Journal on Numerical Analysis 59 (1) 219 (2021)
https://doi.org/10.1137/19M1280740
Energy stable numerical schemes for the fractional-in-space Cahn–Hilliard equation
Linlin Bu, Liquan Mei, Ying Wang and Yan HouApplied Numerical Mathematics 158 392 (2020)
https://doi.org/10.1016/j.apnum.2020.08.007
Arbitrarily high-order linear energy stable schemes for gradient flow models
Yuezheng Gong, Jia Zhao and Qi WangJournal of Computational Physics 419 109610 (2020)
https://doi.org/10.1016/j.jcp.2020.109610
Energy Stable Numerical Schemes for Ternary Cahn-Hilliard System
Wenbin Chen, Cheng Wang, Shufen Wang, Xiaoming Wang and Steven M. WiseJournal of Scientific Computing 84 (2) (2020)
https://doi.org/10.1007/s10915-020-01276-z
A fully coupled mixed finite element method for surfactants spreading on thin liquid films
Yingjie Liu, Christian Peco and John DolbowComputer Methods in Applied Mechanics and Engineering 345 429 (2019)
https://doi.org/10.1016/j.cma.2018.10.045
A Two-Phase Two-Fluxes Degenerate Cahn–Hilliard Model as Constrained Wasserstein Gradient Flow
Clément Cancès, Daniel Matthes and Flore NabetArchive for Rational Mechanics and Analysis 233 (2) 837 (2019)
https://doi.org/10.1007/s00205-019-01369-6
Direct solver for the Cahn–Hilliard equation by Legendre–Galerkin spectral method
Lizhen ChenJournal of Computational and Applied Mathematics 358 34 (2019)
https://doi.org/10.1016/j.cam.2019.03.008
CAHN-HILLIARD VS SINGULAR CAHN-HILLIARD EQUATIONS IN SIMULATIONS OF IMMISCIBLE BINARY FLUIDS
Lizhen ChenJournal of Applied Analysis & Computation 8 (4) 1050 (2018)
https://doi.org/10.11948/2018.1050
A multiphase Cahn–Hilliard–Darcy model for tumour growth with necrosis
Harald Garcke, Kei Fong Lam, Robert Nürnberg and Emanuel SitkaMathematical Models and Methods in Applied Sciences 28 (03) 525 (2018)
https://doi.org/10.1142/S0218202518500148
Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects
Clément Cancès and Flore NabetSpringer 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
On a cross-diffusion model for multiple species with nonlocal interaction and size exclusion
Judith Berendsen, Martin Burger and Jan-Frederik PietschmannNonlinear Analysis 159 10 (2017)
https://doi.org/10.1016/j.na.2017.03.010
Numerical approximation of a non-smooth phase-field model for multicomponent incompressible flow
L’ubomír Baňas and Robert NürnbergESAIM: Mathematical Modelling and Numerical Analysis 51 (3) 1089 (2017)
https://doi.org/10.1051/m2an/2016048
Numerical approximations for a three-component Cahn–Hilliard phase-field model based on the invariant energy quadratization method
Xiaofeng Yang, Jia Zhao, Qi Wang and Jie ShenMathematical Models and Methods in Applied Sciences 27 (11) 1993 (2017)
https://doi.org/10.1142/S0218202517500373
Modeling size controlled nanoparticle precipitation with the co-solvency method by spinodal decomposition
Simon Keßler, Friederike Schmid and Klaus DreseSoft Matter 12 (34) 7231 (2016)
https://doi.org/10.1039/C6SM01198E
Unconditionally energy stable time stepping scheme for Cahn–Morral equation: Application to multi-component spinodal decomposition and optimal space tiling
Rouhollah TavakoliJournal of Computational Physics 304 441 (2016)
https://doi.org/10.1016/j.jcp.2015.10.018
Sharp-Interface Limits of the Cahn--Hilliard Equation with Degenerate Mobility
Alpha Albert Lee, Andreas Münch and Endre SüliSIAM Journal on Applied Mathematics 76 (2) 433 (2016)
https://doi.org/10.1137/140960189
An efficient, unconditionally energy stable local discontinuous Galerkin scheme for the Cahn–Hilliard–Brinkman system
Ruihan Guo and Yan XuJournal of Computational Physics 298 387 (2015)
https://doi.org/10.1016/j.jcp.2015.06.007
Identification of Space-Time Distributed Parameters in the Gierer--Meinhardt Reaction-Diffusion System
Marcus R. Garvie and Catalin TrencheaSIAM Journal on Applied Mathematics 74 (1) 147 (2014)
https://doi.org/10.1137/120885784
Analysis of a time discretization scheme for a nonstandard viscous Cahn–Hilliard system
Pierluigi Colli, Gianni Gilardi, Pavel Krejčí, Paolo Podio-Guidugli and Jürgen SprekelsESAIM: Mathematical Modelling and Numerical Analysis 48 (4) 1061 (2014)
https://doi.org/10.1051/m2an/2014005
An efficient fully-discrete local discontinuous Galerkin method for the Cahn–Hilliard–Hele–Shaw system
Ruihan Guo, Yinhua Xia and Yan XuJournal of Computational Physics 264 23 (2014)
https://doi.org/10.1016/j.jcp.2014.01.037
Efficient numerical solution of discrete multi-component Cahn–Hilliard systems
P. Boyanova and M. NeytchevaComputers & Mathematics with Applications 67 (1) 106 (2014)
https://doi.org/10.1016/j.camwa.2013.10.013
Efficient Solvers of Discontinuous Galerkin Discretization for the Cahn–Hilliard Equations
Ruihan Guo and Yan XuJournal of Scientific Computing 58 (2) 380 (2014)
https://doi.org/10.1007/s10915-013-9738-4
A Time Splitting Space Spectral Element Method for the Cahn-Hilliard Equation
Lizhen Chen and Chuanju XuEast Asian Journal on Applied Mathematics 3 (4) 333 (2013)
https://doi.org/10.4208/eajam.150713.181113a
Phase-Field Models for Multi-Component Fluid Flows
Junseok KimCommunications in Computational Physics 12 (3) 613 (2012)
https://doi.org/10.4208/cicp.301110.040811a
A Quadratic $C^0$ Interior Penalty Method for Linear Fourth Order Boundary Value Problems with Boundary Conditions of the Cahn--Hilliard Type
Susanne C. Brenner, Shiyuan Gu, Thirupathi Gudi and Li-yeng SungSIAM Journal on Numerical Analysis 50 (4) 2088 (2012)
https://doi.org/10.1137/110847469
Numerical simulation and linear well-posedness analysis for a class of three-phase boundary motion problems
Zhenguo Pan and Brian WettonJournal of Computational and Applied Mathematics 236 (13) 3160 (2012)
https://doi.org/10.1016/j.cam.2012.02.013
Parareal in Time Simulation Of Morphological Transformation in Cubic Alloys with Spatially Dependent Composition
Li-Ping He and Minxin HeCommunications in Computational Physics 11 (5) 1697 (2012)
https://doi.org/10.4208/cicp.110310.090911a
Finite element approximation of the Cahn–Hilliard equation on surfaces
Qiang Du, Lili Ju and Li TianComputer Methods in Applied Mechanics and Engineering 200 (29-32) 2458 (2011)
https://doi.org/10.1016/j.cma.2011.04.018
Numerical schemes for a three component Cahn-Hilliard model
Franck Boyer and Sebastian MinjeaudESAIM: Mathematical Modelling and Numerical Analysis 45 (4) 697 (2011)
https://doi.org/10.1051/m2an/2010072
Numerical simulations of immiscible fluid clusters
Robert NürnbergApplied Numerical Mathematics 59 (7) 1612 (2009)
https://doi.org/10.1016/j.apnum.2008.11.003
Error Estimation of a Class of Stable Spectral Approximation to the Cahn-Hilliard Equation
Li-ping HeJournal of Scientific Computing 41 (3) 461 (2009)
https://doi.org/10.1007/s10915-009-9309-x
A numerical method for the ternary Cahn–Hilliard system with a degenerate mobility
Junseok Kim and Kyungkeun KangApplied Numerical Mathematics 59 (5) 1029 (2009)
https://doi.org/10.1016/j.apnum.2008.04.004
A class of stable spectral methods for the Cahn–Hilliard equation
Li-ping He and Yunxian LiuJournal of Computational Physics 228 (14) 5101 (2009)
https://doi.org/10.1016/j.jcp.2009.04.011
A second-order accurate non-linear difference scheme for the N -component Cahn–Hilliard system
Hyun Geun Lee and Junseok KimPhysica A: Statistical Mechanics and its Applications 387 (19-20) 4787 (2008)
https://doi.org/10.1016/j.physa.2008.03.023
Finite Element Approximation of a Three Dimensional Phase Field Model for Void Electromigration
Ľubomír Baňas and Robert NürnbergJournal of Scientific Computing 37 (2) 202 (2008)
https://doi.org/10.1007/s10915-008-9203-y
Finite element approximation of spatially extended predator–prey interactions with the Holling type II functional response
Marcus R. Garvie and Catalin TrencheaNumerische Mathematik 107 (4) 641 (2007)
https://doi.org/10.1007/s00211-007-0106-x
On large time-stepping methods for the Cahn–Hilliard equation
Yinnian He, Yunxian Liu and Tao TangApplied Numerical Mathematics 57 (5-7) 616 (2007)
https://doi.org/10.1016/j.apnum.2006.07.026
Local discontinuous Galerkin methods for the Cahn–Hilliard type equations
Yinhua Xia, Yan Xu and Chi-Wang ShuJournal of Computational Physics 227 (1) 472 (2007)
https://doi.org/10.1016/j.jcp.2007.08.001
Finite Element Approximation of Soluble Surfactant Spreading on a Thin Film
John W. Barrett, Robert Nu?rnberg and Mark R. E. WarnerSIAM Journal on Numerical Analysis 44 (3) 1218 (2006)
https://doi.org/10.1137/040618400
Finite element approximation of a phase field model for surface diffusion of voids in a stressed solid
John Barrett, Harald Garcke and Robert NürnbergMathematics of Computation 75 (253) 7 (2005)
https://doi.org/10.1090/S0025-5718-05-01802-8
Linearized Stability Analysis of Stationary Solutions for Surface Diffusion with Boundary Conditions
Harald Garcke, Kazuo Ito and Yoshihito KohsakaSIAM Journal on Mathematical Analysis 36 (4) 1031 (2005)
https://doi.org/10.1137/S0036141003437939
A Diffuse Interface Model for Alloys with Multiple Components and Phases
Bjorn Stinner, Britta Nestler and Harald GarckeSIAM Journal on Applied Mathematics 64 (3) 775 (2004)
https://doi.org/10.1137/S0036139902413143
Error analysis of a mixed finite element method for the Cahn-Hilliard equation
Xiaobing Feng and Andreas ProhlNumerische Mathematik 99 (1) 47 (2004)
https://doi.org/10.1007/s00211-004-0546-5
Finite Element Approximation of Surfactant Spreading on a Thin Film
John W. Barrett, Harald Garcke and Robert Nu?rnbergSIAM Journal on Numerical Analysis 41 (4) 1427 (2003)
https://doi.org/10.1137/S003614290139799X
Exponential stability for a mirror–symmetric three phase boundary motion by surface diffusion
Joachim Escher, Harald Garcke and Kazuo ItoMathematische Nachrichten 257 (1) 3 (2003)
https://doi.org/10.1002/mana.200310074
Numerical methods for fourth order nonlinear degenerate diffusion problems
Jurgen Becker, Gunther Grun, Martin Lenz and Martin RumpfApplications of Mathematics 47 (6) 517 (2002)
https://doi.org/10.1023/B:APOM.0000034537.55985.44