An unconditionally energy stable second order finite element method for solving the Allen-Cahn equation

[1]  J. Cahn,et al.  A microscopic theory for antiphase boundary motion and its application to antiphase domain coasening , 1979 .

[2]  R. Nicolaides,et al.  Numerical analysis of a continuum model of phase transition , 1991 .

[3]  R. Kobayashi Modeling and numerical simulations of dendritic crystal growth , 1993 .

[4]  I. Steinbach,et al.  A phase field concept for multiphase systems , 1996 .

[5]  A. Karma,et al.  Quantitative phase-field modeling of dendritic growth in two and three dimensions , 1996 .

[6]  Long-Qing Chen,et al.  COMPUTER SIMULATION OF GRAIN GROWTH USING A CONTINUUM FIELD MODEL , 1997 .

[7]  W. Carter,et al.  A continuum model of grain boundaries , 2000 .

[8]  Daisuke Furihata,et al.  A stable and conservative finite difference scheme for the Cahn-Hilliard equation , 2001, Numerische Mathematik.

[9]  A. Karma,et al.  Phase-Field Simulation of Solidification , 2002 .

[10]  Long-Qing Chen,et al.  Computer simulation of 3-D grain growth using a phase-field model , 2002 .

[11]  Weizhu Bao Approximation and comparison for motion by mean curvature with intersection points , 2003 .

[12]  H. Ramanarayan,et al.  Spinodal decomposition in polycrystalline alloys , 2003 .

[13]  Andreas Prohl,et al.  Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows , 2003, Numerische Mathematik.

[14]  K. Mikula,et al.  Geometrical image segmentation by the Allen-Cahn equation , 2004 .

[15]  Haijun Wu,et al.  A Posteriori Error Estimates and an Adaptive Finite Element Method for the Allen–Cahn Equation and the Mean Curvature Flow , 2005, J. Sci. Comput..

[16]  S. Esedoglu,et al.  Threshold dynamics for the piecewise constant Mumford-Shah functional , 2006 .

[17]  Junseok Kim,et al.  An unconditionally gradient stable numerical method for solving the Allen-Cahn equation , 2009 .

[18]  P. Bates,et al.  International Journal of C 2009 Institute for Scientific Numerical Analysis and Modeling Computing and Information Numerical Analysis for a Nonlocal Allen-cahn Equation , 2022 .

[19]  Jian Zhang,et al.  Numerical Studies of Discrete Approximations to the Allen--Cahn Equation in the Sharp Interface Limit , 2009, SIAM J. Sci. Comput..

[20]  Alessandro Tomasi,et al.  Color Image Segmentation by the Vector-Valued Allen–Cahn Phase-Field Model: A Multigrid Solution , 2007, IEEE Transactions on Image Processing.

[21]  Yibao Li,et al.  An unconditionally stable hybrid numerical method for solving the Allen-Cahn equation , 2010, Comput. Math. Appl..

[22]  Xiaofeng Yang,et al.  Numerical approximations of Allen-Cahn and Cahn-Hilliard equations , 2010 .

[23]  Leonardo Golubović,et al.  Interface Dynamics and Far-From-Equilibrium Phase Transitions in Multilayer Epitaxial Growth and Erosion on Crystal Surfaces: Continuum Theory Insights , 2011 .

[24]  Junseok Kim,et al.  A fast, robust, and accurate operator splitting method for phase-field simulations of crystal growth , 2011 .

[25]  Yibao Li,et al.  Multiphase image segmentation using a phase-field model , 2011, Comput. Math. Appl..

[26]  Junseok Kim Phase-Field Models for Multi-Component Fluid Flows , 2012 .

[27]  Charles M. Elliott,et al.  Computation of Two-Phase Biomembranes with Phase Dependent Material Parameters Using Surface Finite Elements , 2013 .

[28]  T. Tang,et al.  Nonlinear stability of the implicit-explicit methods for the Allen-Cahn equation , 2013 .

[29]  Francisco Guillén-González,et al.  Second order schemes and time-step adaptivity for Allen-Cahn and Cahn-Hilliard models , 2014, Comput. Math. Appl..

[30]  Hyun Geun Lee,et al.  Computers and Mathematics with Applications a Semi-analytical Fourier Spectral Method for the Allen–cahn Equation , 2022 .

[31]  June-Yub Lee,et al.  A second order operator splitting method for Allen–Cahn type equations with nonlinear source terms , 2015 .

[32]  Jaemin Shin,et al.  First and second order operator splitting methods for the phase field crystal equation , 2015, J. Comput. Phys..

[33]  Jaemin Shin,et al.  Comparison study of numerical methods for solving the Allen–Cahn equation , 2016 .

[34]  Hehu Xie,et al.  Parameter-Free Time Adaptivity Based on Energy Evolution for the Cahn-Hilliard Equation , 2016 .

[35]  Lijian Jiang,et al.  A reduced order method for Allen-Cahn equations , 2016, J. Comput. Appl. Math..

[36]  Liyong Zhu Efficient and Stable Exponential Runge-Kutta Methods for Parabolic Equations , 2017 .

[37]  Jiang Yang,et al.  The scalar auxiliary variable (SAV) approach for gradient flows , 2018, J. Comput. Phys..