EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues ESAIM: M2AN, 38 1 (2004) 129-142 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:

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

Encyclopedia of Computational Mechanics Second Edition

Hector Gomez and Kristoffer G. van der Zee
Encyclopedia of Computational Mechanics Second Edition 1 (2017)
DOI: 10.1002/9781119176817.ecm2118
See this article

An adaptive variational procedure for the conservative and positivity preserving Allen–Cahn phase-field model

Vaibhav Joshi and Rajeev K. Jaiman
Journal of Computational Physics 366 478 (2018)
DOI: 10.1016/j.jcp.2018.04.022
See this article

A SCR-based error estimation and adaptive finite element method for the Allen–Cahn equation

Yaoyao Chen, Yunqing Huang and Nianyu Yi
Computers & Mathematics with Applications 78 (1) 204 (2019)
DOI: 10.1016/j.camwa.2019.02.022
See this article

Structure Preserving Discretization of Allen–Cahn Type Problems Modeling the Motion of Phase Boundaries

Anke Böttcher and Herbert Egger
Vietnam Journal of Mathematics 48 (4) 847 (2020)
DOI: 10.1007/s10013-020-00428-w
See this article

Recovery type a posteriori error estimation of adaptive finite element method for Allen–Cahn equation

Yaoyao Chen, Yunqing Huang and Nianyu Yi
Journal of Computational and Applied Mathematics 369 112574 (2020)
DOI: 10.1016/j.cam.2019.112574
See this article

Error Analysis of an Unconditionally Energy Stable Local Discontinuous Galerkin Scheme for the Cahn–Hilliard Equation with Concentration-Dependent Mobility

Fengna Yan and Yan Xu
Computational Methods in Applied Mathematics 21 (3) 729 (2021)
DOI: 10.1515/cmam-2020-0066
See this article

Numerical Methods for Nonlinear Partial Differential Equations

Sören Bartels
Springer Series in Computational Mathematics, Numerical Methods for Nonlinear Partial Differential Equations 47 153 (2015)
DOI: 10.1007/978-3-319-13797-1_6
See this article

Numerical Studies of Discrete Approximations to the Allen–Cahn Equation in the Sharp Interface Limit

Jian Zhang and Qiang Du
SIAM Journal on Scientific Computing 31 (4) 3042 (2009)
DOI: 10.1137/080738398
See this article

On Efficient Second Order Stabilized Semi-implicit Schemes for the Cahn–Hilliard Phase-Field Equation

Lin Wang and Haijun Yu
Journal of Scientific Computing 77 (2) 1185 (2018)
DOI: 10.1007/s10915-018-0746-2
See this article

Error estimates for time discretizations of Cahn–Hilliard and Allen–Cahn phase-field models for two-phase incompressible flows

Yongyong Cai, Heejun Choi and Jie Shen
Numerische Mathematik 137 (2) 417 (2017)
DOI: 10.1007/s00211-017-0875-9
See this article

Numerical analysis for phase field simulations of moving interfaces with topological changes

Sören Bartels and Rüdiger Müller
PAMM 10 (1) 565 (2010)
DOI: 10.1002/pamm.201010275
See this article

Robust Error Estimates for Adaptive Phase Field Simulations

Sören Bartels and Rüdiger Müller
PAMM 8 (1) 10983 (2008)
DOI: 10.1002/pamm.200810983
See this article

Duality-based two-level error estimation for time-dependent PDEs: Application to linear and nonlinear parabolic equations

G. Şimşek, X. Wu, K.G. van der Zee and E.H. van Brummelen
Computer Methods in Applied Mechanics and Engineering 288 83 (2015)
DOI: 10.1016/j.cma.2014.11.019
See this article

Error control for the approximation of Allen–Cahn and Cahn–Hilliard equations with a logarithmic potential

Sören Bartels and Rüdiger Müller
Numerische Mathematik 119 (3) 409 (2011)
DOI: 10.1007/s00211-011-0389-9
See this article

Discontinuous Galerkin Methods for Mass Transfer through Semipermeable Membranes

Andrea Cangiani, Emmanuil H. Georgoulis and Max Jensen
SIAM Journal on Numerical Analysis 51 (5) 2911 (2013)
DOI: 10.1137/120890429
See this article

Robustness of error estimates for phase field models at a class of topological changes

Sören Bartels
Computer Methods in Applied Mechanics and Engineering 288 75 (2015)
DOI: 10.1016/j.cma.2014.11.005
See this article

Preconditioning for Allen–Cahn variational inequalities with non-local constraints

Luise Blank, Lavinia Sarbu and Martin Stoll
Journal of Computational Physics 231 (16) 5406 (2012)
DOI: 10.1016/j.jcp.2012.04.035
See this article

Decoupled Energy Stable Schemes for Phase-Field Models of Two-Phase Complex Fluids

Jie Shen and Xiaofeng Yang
SIAM Journal on Scientific Computing 36 (1) B122 (2014)
DOI: 10.1137/130921593
See this article

Energy Stable Numerical Schemes for a Hydrodynamic Model of Nematic Liquid Crystals

Jia Zhao, Xiaofeng Yang, Jun Li and Qi Wang
SIAM Journal on Scientific Computing 38 (5) A3264 (2016)
DOI: 10.1137/15M1024093
See this article

Analysis of symmetric interior penalty discontinuous Galerkin methods for the Allen–Cahn equation and the mean curvature flow

Xiaobing Feng and Yukun Li
IMA Journal of Numerical Analysis 35 (4) 1622 (2015)
DOI: 10.1093/imanum/dru058
See this article

hp-Adaptive Galerkin Time Stepping Methods for Nonlinear Initial Value Problems

Irene Kyza, Stephen Metcalfe and Thomas P. Wihler
Journal of Scientific Computing 75 (1) 111 (2018)
DOI: 10.1007/s10915-017-0565-x
See this article

A three level linearized compact difference scheme for the Cahn-Hilliard equation

Juan Li, ZhiZhong Sun and Xuan Zhao
Science China Mathematics 55 (4) 805 (2012)
DOI: 10.1007/s11425-011-4290-x
See this article

An adaptive time stepping method with efficient error control for second-order evolution problems

JianGuo Huang, JunJiang Lai and Tao Tang
Science China Mathematics 56 (12) 2753 (2013)
DOI: 10.1007/s11425-013-4730-x
See this article

Fast Explicit Integration Factor Methods for Semilinear Parabolic Equations

Lili Ju, Jian Zhang, Liyong Zhu and Qiang Du
Journal of Scientific Computing 62 (2) 431 (2015)
DOI: 10.1007/s10915-014-9862-9
See this article

Geometric Partial Differential Equations - Part I

Eberhard Bänsch and Alfred Schmidt
Handbook of Numerical Analysis, Geometric Partial Differential Equations - Part I 21 555 (2020)
DOI: 10.1016/bs.hna.2019.05.004
See this article

Geometric Partial Differential Equations - Part I

Qiang Du and Xiaobing Feng
Handbook of Numerical Analysis, Geometric Partial Differential Equations - Part I 21 425 (2020)
DOI: 10.1016/bs.hna.2019.05.001
See this article

Pointwise a Posteriori Error Bounds for Blow-Up in the Semilinear Heat Equation

Irene Kyza and Stephen Metcalfe
SIAM Journal on Numerical Analysis 58 (5) 2609 (2020)
DOI: 10.1137/19M1264758
See this article

Decoupled, Energy Stable Schemes for Phase-Field Models of Two-Phase Incompressible Flows

Jie Shen and Xiaofeng Yang
SIAM Journal on Numerical Analysis 53 (1) 279 (2015)
DOI: 10.1137/140971154
See this article

Error Estimates for a Finite Element Discretization of a Two‐Scale Phase Field Model

Christof Eck
Multiscale Modeling & Simulation 6 (1) 1 (2007)
DOI: 10.1137/060656942
See this article

Adaptivity and Blow-Up Detection for Nonlinear Evolution Problems

Andrea Cangiani, Emmanuil H. Georgoulis, Irene Kyza and Stephen Metcalfe
SIAM Journal on Scientific Computing 38 (6) A3833 (2016)
DOI: 10.1137/16M106073X
See this article

Robust A Priori and A Posteriori Error Analysis for the Approximation of Allen–Cahn and Ginzburg–Landau Equations Past Topological Changes

Sören Bartels, Rüdiger Müller and Christoph Ortner
SIAM Journal on Numerical Analysis 49 (1) 110 (2011)
DOI: 10.1137/090751530
See this article

Analysis for Time Discrete Approximations of Blow-up Solutions of Semilinear Parabolic Equations

Irene Kyza and Charalambos Makridakis
SIAM Journal on Numerical Analysis 49 (1) 405 (2011)
DOI: 10.1137/100796819
See this article

Error estimates for fully discrete BDF finite element approximations of the Allen–Cahn equation

Georgios Akrivis and Buyang Li
IMA Journal of Numerical Analysis (2020)
DOI: 10.1093/imanum/draa065
See this article

A Posteriori Error Estimates for the Allen--Cahn Problem

Konstantinos Chrysafinos, Emmanuil H. Georgoulis and Dimitra Plaka
SIAM Journal on Numerical Analysis 58 (5) 2662 (2020)
DOI: 10.1137/19M1277540
See this article

Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 2

Jie Shen
Handbook of Numerical Analysis, Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 2 20 647 (2019)
DOI: 10.1016/bs.hna.2019.06.004
See this article

Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows

Jie Shen and Jie Xu
SIAM Journal on Numerical Analysis 56 (5) 2895 (2018)
DOI: 10.1137/17M1159968
See this article

Numerical approximations to a new phase field model for two phase flows of complex fluids

Jia Zhao, Qi Wang and Xiaofeng Yang
Computer Methods in Applied Mechanics and Engineering 310 77 (2016)
DOI: 10.1016/j.cma.2016.06.008
See this article

A second order operator splitting method for Allen–Cahn type equations with nonlinear source terms

Hyun Geun Lee and June-Yub Lee
Physica A: Statistical Mechanics and its Applications 432 24 (2015)
DOI: 10.1016/j.physa.2015.03.012
See this article

Robust Multigrid Methods for Vector-valued Allen–Cahn Equations with Logarithmic Free Energy

Ralf Kornhuber and Rolf Krause
Computing and Visualization in Science 9 (2) 103 (2006)
DOI: 10.1007/s00791-006-0020-2
See this article

Robust a-posteriori error control of Cahn-Hilliard type equations with elasticity

Sören Bartels and Rüdiger Müller
PAMM 7 (1) 1023305 (2007)
DOI: 10.1002/pamm.200700915
See this article

Energy stable schemes for Cahn-Hilliard phase-field model of two-phase incompressible flows

Jie Shen and Xiaofeng Yang
Chinese Annals of Mathematics, Series B 31 (5) 743 (2010)
DOI: 10.1007/s11401-010-0599-y
See this article

A review on computational modelling of phase-transition problems

Hector Gomez, Miguel Bures and Adrian Moure
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377 (2143) 20180203 (2019)
DOI: 10.1098/rsta.2018.0203
See this article

A linearly second-order energy stable scheme for the phase field crystal model

Shuaichao Pei, Yanren Hou and Bo You
Applied Numerical Mathematics 140 134 (2019)
DOI: 10.1016/j.apnum.2019.01.017
See this article

Goal-oriented error estimation for Cahn-Hilliard models of binary phase transition

Kristoffer G. van der Zee, J. Tinsley Oden, Serge Prudhomme and Andrea Hawkins-Daarud
Numerical Methods for Partial Differential Equations 27 (1) 160 (2011)
DOI: 10.1002/num.20638
See this article

A diffuse interface model for two-phase ferrofluid flows

Ricardo H. Nochetto, Abner J. Salgado and Ignacio Tomas
Computer Methods in Applied Mechanics and Engineering 309 497 (2016)
DOI: 10.1016/j.cma.2016.06.011
See this article

A Posteriori Error Estimates and an Adaptive Finite Element Method for the Allen–Cahn Equation and the Mean Curvature Flow

Xiaobing Feng and Hai-jun Wu
Journal of Scientific Computing 24 (2) 121 (2005)
DOI: 10.1007/s10915-004-4610-1
See this article

Numerical Mathematics and Advanced Applications 2009

Carsten Gräser, Ralf Kornhuber and Uli Sack
Numerical Mathematics and Advanced Applications 2009 397 (2010)
DOI: 10.1007/978-3-642-11795-4_42
See this article

Numerical Approximations for Allen-Cahn Type Phase Field Model of Two-Phase Incompressible Fluids with Moving Contact Lines

Lina Ma, Rui Chen, Xiaofeng Yang and Hui Zhang
Communications in Computational Physics 21 (3) 867 (2017)
DOI: 10.4208/cicp.OA-2016-0008
See this article

Interior Penalty Discontinuous Galerkin Based Isogeometric Analysis for Allen-Cahn Equations on Surfaces

Futao Zhang, Yan Xu, Falai Chen and Ruihan Guo
Communications in Computational Physics 18 (5) 1380 (2015)
DOI: 10.4208/cicp.010914.180315a
See this article

Stability analysis and best approximation error estimates of discontinuous time-stepping schemes for the Allen–Cahn equation

Konstantinos Chrysafinos
ESAIM: Mathematical Modelling and Numerical Analysis 53 (2) 551 (2019)
DOI: 10.1051/m2an/2018071
See this article

Space–time discontinuous Galerkin methods for the ε-dependent stochastic Allen–Cahn equation with mild noise

Dimitra C Antonopoulou
IMA Journal of Numerical Analysis 40 (3) 2076 (2020)
DOI: 10.1093/imanum/drz019
See this article

A Posteriori Error Estimation and Adaptivity for Nonlinear Parabolic Equations using IMEX-Galerkin Discretization of Primal and Dual Equations

X. Wu, K. G. van der Zee, G. Simsek and E. H. van Brummelen
SIAM Journal on Scientific Computing 40 (5) A3371 (2018)
DOI: 10.1137/17M1133968
See this article

Multiscale model reduction for the Allen–Cahn problem in perforated domains

Aleksei Tyrylgin, Yaoyao Chen, Maria Vasilyeva and Eric T. Chung
Journal of Computational and Applied Mathematics 381 113010 (2021)
DOI: 10.1016/j.cam.2020.113010
See this article

Optimal error estimates for the scalar auxiliary variable finite-element schemes for gradient flows

Hongtao Chen, Jingjing Mao and Jie Shen
Numerische Mathematik 145 (1) 167 (2020)
DOI: 10.1007/s00211-020-01112-4
See this article

Robusta priorierror analysis for the approximation of degree-one Ginzburg-Landau vortices

Sören Bartels
ESAIM: Mathematical Modelling and Numerical Analysis 39 (5) 863 (2005)
DOI: 10.1051/m2an:2005038
See this article

An energy stable linear diffusive Crank–Nicolson scheme for the Cahn–Hilliard gradient flow

Lin Wang and Haijun Yu
Journal of Computational and Applied Mathematics 377 112880 (2020)
DOI: 10.1016/j.cam.2020.112880
See this article

ANALYSIS OF STABILITY AND ERROR ESTIMATES FOR THREE METHODS APPROXIMATING A NONLINEAR REACTION-DIFFUSION EQUATION

Journal of Applied Analysis & Computation 7 (1) 1 (2017)
DOI: 10.11948/2017001
See this article

On a posteriori error control for the Allen-Cahn problem

Emmanuil H. Georgoulis and Charalambos Makridakis
Mathematical Methods in the Applied Sciences 37 (2) 173 (2014)
DOI: 10.1002/mma.2894
See this article

Stabilized semi-implicit spectral deferred correction methods for Allen-Cahn and Cahn-Hilliard equations

Fei Liu and Jie Shen
Mathematical Methods in the Applied Sciences 38 (18) 4564 (2015)
DOI: 10.1002/mma.2869
See this article

Numerical analysis of a second-order IPDGFE method for the Allen–Cahn equation and the curvature-driven geometric flow

Huanrong Li, Zhengyuan Song and Junzhao Hu
Computers & Mathematics with Applications 86 49 (2021)
DOI: 10.1016/j.camwa.2021.01.014
See this article

Efficient energy stable numerical schemes for a phase field moving contact line model

Jie Shen, Xiaofeng Yang and Haijun Yu
Journal of Computational Physics 284 617 (2015)
DOI: 10.1016/j.jcp.2014.12.046
See this article

A decoupled energy stable scheme for a hydrodynamic phase-field model of mixtures of nematic liquid crystals and viscous fluids

Jia Zhao, Xiaofeng Yang, Jie Shen and Qi Wang
Journal of Computational Physics 305 539 (2016)
DOI: 10.1016/j.jcp.2015.09.044
See this article

Unconditionally energy stable large time stepping method for the L2-gradient flow based ternary phase-field model with precise nonlocal volume conservation

Jun Zhang and Xiaofeng Yang
Computer Methods in Applied Mechanics and Engineering 361 112743 (2020)
DOI: 10.1016/j.cma.2019.112743
See this article

Some algorithms for the mean curvature flow under topological changes

Arthur Bousquet, Yukun Li and Guanqian Wang
Computational and Applied Mathematics 40 (4) (2021)
DOI: 10.1007/s40314-021-01494-7
See this article

A posteriori error analysis for time-dependent Ginzburg-Landau type equations

S�ren Bartels
Numerische Mathematik 99 (4) 557 (2005)
DOI: 10.1007/s00211-004-0560-7
See this article