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

被引：56

作者：

Liu, Fei ^{[1
]}

Shen, Jie ^{[2
,3
]}

机构：

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

[2] Xiamen Univ, Sch Math Sci, Xiamen, Peoples R China

[3] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2015年 / 38卷 / 18期

基金：

美国国家科学基金会; 中国国家自然科学基金;

关键词：

spectral deferred correction; spectral Galerkin method; method of lines; Allen-Cahn and Cahn-Hilliard equations; PHASE-FIELD MODEL; THIN-FILM EPITAXY; PARABOLIC PROBLEMS; GALERKIN METHOD; TIME; APPROXIMATION; EVOLUTION; MOBILITY; GROWTH; ORDER;

D O I：

10.1002/mma.2869

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Stabilized semi-implicit spectral deferred correction methods are constructed for the time discretization of Allen-Cahn and Cahn-Hilliard equations. These methods are unconditionally stable, lead to simple linear system to solve at each iteration, and can achieve high-order time accuracy with a few iterations in each time step. Ample numerical results are presented to demonstrate the effectiveness of the stabilized semi-implicit spectral deferred correction methods for solving the Allen-Cahn and Cahn-Hilliard equations. Copyright (C) 2013 John Wiley & Sons, Ltd.

引用

页码：4564 / 4575

页数：12

共 50 条

[21] Comparative study of the lattice Boltzmann models for Allen-Cahn and Cahn-Hilliard equations
Wang, H. L.
Chai, Z. H.
Shi, B. C.
Liang, H.
PHYSICAL REVIEW E, 2016, 94 (03)
[22] The Cahn-Hilliard/Allen-Cahn equation with inertial and proliferation terms
Sen, Zehra
Khanmamedov, Azer
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 530 (02)
[23] On the viscous Allen-Cahn and Cahn-Hilliard systems with willmore regularization
Makki, Ahmad
APPLICATIONS OF MATHEMATICS, 2016, 61 (06) : 685 - 725
[24] THE EXISTENCE OF GLOBAL ATTRACTOR FOR A CAHN-HILLIARD/ALLEN-CAHN EQUATION
Tang, H.
Liu, C.
Zhao, Z.
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2016, 42 (03): : 643 - 658
[25] ASYMPTOTIC BEHAVIOR OF A CAHN-HILLIARD/ALLEN-CAHN SYSTEM WITH TEMPERATURE
Miranville, Alain
Quintanilla, Ramon
Saoud, Wafa
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2020, 19 (04) : 2257 - 2288
[26] ON THE STEADY STATE BIFURCATION OF THE CAHN-HILLIARD/ALLEN-CAHN SYSTEM
Li, Shixing
Yan, Dongming
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (07): : 3077 - 3088
[27] Finite element approximation of an Allen-Cahn/Cahn-Hilliard system
Barrett, JW
Blowey, JF
IMA JOURNAL OF NUMERICAL ANALYSIS, 2002, 22 (01) : 11 - 71
[28] On the viscous Allen-Cahn and Cahn-Hilliard systems with willmore regularization
Ahmad Makki
Applications of Mathematics, 2016, 61 : 685 - 725
[29] ON THE STABILIZATION SIZE OF SEMI-IMPLICIT FOURIER-SPECTRAL METHODS FOR 3D CAHN-HILLIARD EQUATIONS
Li, Dong
Qiao, Zhonghua
COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2017, 15 (06) : 1489 - 1506
[30] THE STABILIZED SEMI-IMPLICIT FINITE ELEMENT METHOD FOR THE SURFACE ALLEN-CAHN EQUATION
Xiao, Xufeng
Feng, Xinlong
Yuan, Jinyun
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2017, 22 (07): : 2857 - 2877

← 1 2 3 4 5 →