EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues ESAIM: M2AN, 47 5 (2013) 1413-1432 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):

Magnetically Enhanced Thin‐Film Coarsening by a Magnetic XPFC Model Allowing to Decouple Magnetic Anisotropy and Magnetostriction

Rainer Backofen and Axel Voigt
Advanced Engineering Materials 25 (18) (2023)
DOI: 10.1002/adem.202201926
See this article

A multiphase Cahn–Hilliard system with mobilities and the numerical simulation of dewetting

Elie Bretin, Roland Denis, Simon Masnou, Arnaud Sengers and Garry Terii
ESAIM: Mathematical Modelling and Numerical Analysis 57 (3) 1473 (2023)
DOI: 10.1051/m2an/2023023
See this article

Evaluation of mechanical properties of triple-junction-free polycrystalline graphene

Jeonghyeon Heo and Jihoon Han
Nanotechnology 34 (41) 415704 (2023)
DOI: 10.1088/1361-6528/ace44e
See this article

Design and mathematical modeling of polymeric phases to obtain controlled microporosity materials by 3D printing

Marco A. Morales, Sinhue Ruiz-Salgado, Ricardo Agustín-Serrano, Benito Zenteno-Mateo and José I. Rodríguez-Mora
Progress in Additive Manufacturing (2023)
DOI: 10.1007/s40964-023-00437-4
See this article

An energy-stable second-order finite element method for the Swift–Hohenberg equation

Longzhao Qi and Yanren Hou
Computational and Applied Mathematics 42 (1) (2023)
DOI: 10.1007/s40314-022-02144-2
See this article

Amplitude expansion of the phase-field crystal model for complex crystal structures

Marcello De Donno, Lucas Benoit–Maréchal and Marco Salvalaglio
Physical Review Materials 7 (3) (2023)
DOI: 10.1103/PhysRevMaterials.7.033804
See this article

A mobility-SAV approach for a Cahn-Hilliard equation with degenerate mobilities

Elie Bretin, Luca Calatroni and Simon Masnou
Discrete and Continuous Dynamical Systems - S (2023)
DOI: 10.3934/dcdss.2023177
See this article

Efficient and energy stable numerical schemes for the two-mode phase field crystal equation

Fan Zhang, Dongfang Li and Hai-Wei Sun
Journal of Computational and Applied Mathematics 427 115148 (2023)
DOI: 10.1016/j.cam.2023.115148
See this article

Spectral deferred correction method for Landau–Brazovskii model with convex splitting technique

Donghang Zhang and Lei Zhang
Journal of Computational Physics 491 112348 (2023)
DOI: 10.1016/j.jcp.2023.112348
See this article

Improved time integration for phase‐field crystal models of solidification

Maik Punke, Steven M. Wise, Axel Voigt and Marco Salvalaglio
PAMM 23 (1) (2023)
DOI: 10.1002/pamm.202200112
See this article

Explicit temperature coupling in phase-field crystal models of solidification

Maik Punke, Steven M Wise, Axel Voigt and Marco Salvalaglio
Modelling and Simulation in Materials Science and Engineering 30 (7) 074004 (2022)
DOI: 10.1088/1361-651X/ac8abd
See this article

Microscopic patterns in the 2D phase-field-crystal model

Gabriel Martine-La Boissonière, Rustum Choksi and Jean-Philippe Lessard
Nonlinearity 35 (3) 1500 (2022)
DOI: 10.1088/1361-6544/ac4d91
See this article

Magnetic APFC modeling and the influence of magneto-structural interactions on grain shrinkage

Rainer Backofen, Marco Salvalaglio and Axel Voigt
Modelling and Simulation in Materials Science and Engineering 30 (6) 064003 (2022)
DOI: 10.1088/1361-651X/ac773a
See this article

A stabilized fully-discrete scheme for phase field crystal equation

Fan Zhang, Dongfang Li, Hai-Wei Sun and Jia-Li Zhang
Applied Numerical Mathematics 178 337 (2022)
DOI: 10.1016/j.apnum.2022.04.007
See this article

Numerical scheme for solving the nonuniformly forced cubic and quintic Swift–Hohenberg equations strictly respecting the Lyapunov functional

D.L. Coelho, E. Vitral, J. Pontes and N. Mangiavacchi
Journal of Computational and Applied Mathematics 407 114005 (2022)
DOI: 10.1016/j.cam.2021.114005
See this article

A non-iterative and unconditionally energy stable method for the Swift–Hohenberg equation with quadratic–cubic nonlinearity

Hyun Geun Lee
Applied Mathematics Letters 123 107579 (2022)
DOI: 10.1016/j.aml.2021.107579
See this article

Three Explicit and Implicit Runge-Kutta Methods for Fractional Conservation Swift-Hohenberg Equation

婷 李
Advances in Applied Mathematics 11 (04) 2221 (2022)
DOI: 10.12677/AAM.2022.114236
See this article

Unconditionally energy stable C0-virtual element scheme for solving generalized Swift-Hohenberg equation

Mehdi Dehghan, Zeinab Gharibi and Mohammad Reza Eslahchi
Applied Numerical Mathematics 178 304 (2022)
DOI: 10.1016/j.apnum.2022.03.013
See this article

Approximation of surface diffusion flow: A second-order variational Cahn–Hilliard model with degenerate mobilities

Elie Bretin, Simon Masnou, Arnaud Sengers and Garry Terii
Mathematical Models and Methods in Applied Sciences 32 (04) 793 (2022)
DOI: 10.1142/S0218202522500178
See this article

Stability and convergence analysis for a new phase field crystal model with a nonlocal Lagrange multiplier

Shimin Lin, Junying Cao, Jun Zhang and Tao Sun
Mathematical Methods in the Applied Sciences 44 (6) 4972 (2021)
DOI: 10.1002/mma.7080
See this article

A comparison of different approaches to enforce lattice symmetry in two‐dimensional crystals

Rainer Backofen, Lisa Sahlmann, Anna Willmann and Axel Voigt
PAMM 20 (1) (2021)
DOI: 10.1002/pamm.202000192
See this article

A nonlinear fourth-order PDE for image denoising in Sobolev spaces with variable exponents and its numerical algorithm

Hamdi Houichet, Anis Theljani and Maher Moakher
Computational and Applied Mathematics 40 (3) (2021)
DOI: 10.1007/s40314-021-01462-1
See this article

A Second Order Energy Stable BDF Numerical Scheme for the Swift–Hohenberg Equation

Longzhao Qi and Yanren Hou
Journal of Scientific Computing 88 (3) (2021)
DOI: 10.1007/s10915-021-01593-x
See this article

A Fast and Efficient Numerical Algorithm for the Nonlocal Conservative Swift–Hohenberg Equation

Jingying Wang and Shuying Zhai
Mathematical Problems in Engineering 2020 1 (2020)
DOI: 10.1155/2020/7012483
See this article

Arbitrarily high-order linear energy stable schemes for gradient flow models

Yuezheng Gong, Jia Zhao and Qi Wang
Journal of Computational Physics 419 109610 (2020)
DOI: 10.1016/j.jcp.2020.109610
See this article

Linear second order energy stable schemes for phase field crystal growth models with nonlocal constraints

Xiaobo Jing and Qi Wang
Computers & Mathematics with Applications 79 (3) 764 (2020)
DOI: 10.1016/j.camwa.2019.07.030
See this article

Arbitrarily High-Order Unconditionally Energy Stable Schemes for Thermodynamically Consistent Gradient Flow Models

Yuezheng Gong, Jia Zhao and Qi Wang
SIAM Journal on Scientific Computing 42 (1) B135 (2020)
DOI: 10.1137/18M1213579
See this article

A meshless technique based on generalized moving least squares combined with the second-order semi-implicit backward differential formula for numerically solving time-dependent phase field models on the spheres

Vahid Mohammadi and Mehdi Dehghan
Applied Numerical Mathematics 153 248 (2020)
DOI: 10.1016/j.apnum.2020.02.012
See this article

An adaptive Cahn-Hilliard equation for enhanced edges in binary image inpainting

Anis Theljani, Hamdi Houichet and Anis Mohamed
Journal of Algorithms & Computational Technology 14 174830262094143 (2020)
DOI: 10.1177/1748302620941430
See this article

Parallel energy-stable phase field crystal simulations based on domain decomposition methods

Ying Wei, Chao Yang and Jizu Huang
Computer Physics Communications 234 26 (2019)
DOI: 10.1016/j.cpc.2018.08.006
See this article

Statistics of grain growth: Experiment versus the phase-field-crystal and Mullins models

Gabriel Martine La Boissonière, Rustum Choksi, Katayun Barmak and Selim Esedoḡlu
Materialia 6 100280 (2019)
DOI: 10.1016/j.mtla.2019.100280
See this article

Numerical Simulation of Pattern Formation on Surfaces Using an Efficient Linear Second-Order Method

Hyun Geun Lee
Symmetry 11 (8) 1010 (2019)
DOI: 10.3390/sym11081010
See this article

An energy stable method for the Swift–Hohenberg equation with quadratic–cubic nonlinearity

Hyun Geun Lee
Computer Methods in Applied Mechanics and Engineering 343 40 (2019)
DOI: 10.1016/j.cma.2018.08.019
See this article

Unconditional stability for multistep ImEx schemes: Practice

Benjamin Seibold, David Shirokoff and Dong Zhou
Journal of Computational Physics 376 295 (2019)
DOI: 10.1016/j.jcp.2018.09.044
See this article

Atom based grain extraction and measurement of geometric properties

Gabriel Martine La Boissonière and Rustum Choksi
Modelling and Simulation in Materials Science and Engineering 26 (3) 035001 (2018)
DOI: 10.1088/1361-651X/aaa635
See this article

Grain extraction and microstructural analysis method for two-dimensional poly and quasicrystalline solids

Petri Hirvonen, Gabriel Martine La Boissonière, Zheyong Fan, et al.
Physical Review Materials 2 (10) (2018)
DOI: 10.1103/PhysRevMaterials.2.103603
See this article

Convex splitting method for the calculation of transition states of energy functional

Shuting Gu and Xiang Zhou
Journal of Computational Physics 353 417 (2018)
DOI: 10.1016/j.jcp.2017.10.028
See this article

The meshless local collocation method for solving multi-dimensional Cahn-Hilliard, Swift-Hohenberg and phase field crystal equations

Mehdi Dehghan and Mostafa Abbaszadeh
Engineering Analysis with Boundary Elements 78 49 (2017)
DOI: 10.1016/j.enganabound.2017.02.005
See this article

Unconditional Stability for Multistep ImEx Schemes: Theory

Rodolfo R. Rosales, Benjamin Seibold, David Shirokoff and Dong Zhou
SIAM Journal on Numerical Analysis 55 (5) 2336 (2017)
DOI: 10.1137/16M1094324
See this article

A semi-analytical Fourier spectral method for the Swift–Hohenberg equation

Hyun Geun Lee
Computers & Mathematics with Applications 74 (8) 1885 (2017)
DOI: 10.1016/j.camwa.2017.06.053
See this article

An efficient and stable compact fourth-order finite difference scheme for the phase field crystal equation

Yibao Li and Junseok Kim
Computer Methods in Applied Mechanics and Engineering 319 194 (2017)
DOI: 10.1016/j.cma.2017.02.022
See this article

Unconditionally energy stable time stepping scheme for Cahn–Morral equation: Application to multi-component spinodal decomposition and optimal space tiling

Rouhollah Tavakoli
Journal of Computational Physics 304 441 (2016)
DOI: 10.1016/j.jcp.2015.10.018
See this article

Energy stable and convergent finite element schemes for the modified phase field crystal equation

Maurizio Grasselli and Morgan Pierre
ESAIM: Mathematical Modelling and Numerical Analysis 50 (5) 1523 (2016)
DOI: 10.1051/m2an/2015092
See this article

Phase-field crystal equation with memory

Monica Conti, Andrea Giorgini and Maurizio Grasselli
Journal of Mathematical Analysis and Applications 436 (2) 1297 (2016)
DOI: 10.1016/j.jmaa.2015.12.056
See this article

A Review of Quantitative Phase-Field Crystal Modeling of Solid–Liquid Structures

Ebrahim Asadi and Mohsen Asle Zaeem
JOM 67 (1) 186 (2015)
DOI: 10.1007/s11837-014-1232-4
See this article

Development and Analysis of a Block-Preconditioner for the Phase-Field Crystal Equation

Simon Praetorius and Axel Voigt
SIAM Journal on Scientific Computing 37 (3) B425 (2015)
DOI: 10.1137/140980375
See this article

Crystal Image Analysis Using 2D Synchrosqueezed Transforms

Haizhao Yang, Jianfeng Lu and Lexing Ying
Multiscale Modeling & Simulation 13 (4) 1542 (2015)
DOI: 10.1137/140955872
See this article

Fast Automated Detection of Crystal Distortion and Crystal Defects in Polycrystal Images

Matt Elsey and Benedikt Wirth
Multiscale Modeling & Simulation 12 (1) 1 (2014)
DOI: 10.1137/130916515
See this article

Capturing the complex physics behind universal grain size distributions in thin metallic films

R. Backofen, K. Barmak, K.E. Elder and A. Voigt
Acta Materialia 64 72 (2014)
DOI: 10.1016/j.actamat.2013.11.034
See this article

Well-posedness and long-time behavior for the modified phase-field crystal equation

Maurizio Grasselli and Hao Wu
Mathematical Models and Methods in Applied Sciences 24 (14) 2743 (2014)
DOI: 10.1142/S0218202514500365
See this article