Stable second-order schemes for the space-fractional Cahn-Hilliard and Allen-Cahn equations

被引：27

作者：

Bu, Linlin ^{[1
]}

Mei, Liquan ^{[1
]}

Hou, Yan ^{[2
]}

机构：

[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China

[2] Shenzhen Yun Zhong Fei Network Technol Co Ltd, Shenzhen 518000, Guangdong, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2019年 / 78卷 / 11期

关键词：

Fractional Cahn-Hilliard equation; Fractional Allen-Cahn equation; Convex splitting; Mass conservative; The unique solvability; Energy stable; FINITE-DIFFERENCE SCHEME; SPLITTING METHODS; FREE-ENERGY;

D O I：

10.1016/j.camwa.2019.05.016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose stable second-order numerical schemes for the fractional Cahn-Hilliard and Allen-Cahn equations, which are based on the convex splitting in time and the Fourier spectral method in space. It is shown that the scheme for the fractional Cahn-Hilliard equation preserves mass. Meanwhile, the unique solvability and energy stability of the numerical schemes for the fractional Cahn-Hilliard and Allen-Cahn equations are proved. Finally, we present some numerical experiments to confirm the accuracy and the effectiveness of the proposed methods. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页码：3485 / 3500

页数：16

共 28 条

[1] ANALYSIS AND APPROXIMATION OF A FRACTIONAL CAHN-HILLIARD EQUATION [J].

Ainsworth, Mark ;

Mao, Zhiping .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2017, 55 (04) :1689-1718

[2] Well-posedness of the Cahn-Hilliard equation with fractional free energy and its Fourier Galerkin approximation [J].

Ainsworth, Mark ;

Mao, Zhiping .

CHAOS SOLITONS & FRACTALS, 2017, 102 :264-273

[3] Fractional Cahn-Hilliard, Allen-Calm and porous medium equations [J].

Akagi, Goro ;

Schimperna, Giulio ;

Segatti, Antonio .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 261 (06) :2935-2985

[4] MICROSCOPIC THEORY FOR ANTIPHASE BOUNDARY MOTION AND ITS APPLICATION TO ANTIPHASE DOMAIN COARSENING [J].

ALLEN, SM ;

CAHN, JW .

ACTA METALLURGICA, 1979, 27 (06) :1085-1095

[5] A Fractional Inpainting Model Based on the Vector-Valued Cahn-Hilliard Equation [J].

Bosch, Jessica ;

Stoll, Martin .

SIAM JOURNAL ON IMAGING SCIENCES, 2015, 8 (04) :2352-2382

[6] FREE ENERGY OF A NONUNIFORM SYSTEM .1. INTERFACIAL FREE ENERGY [J].

CAHN, JW ;

HILLIARD, JE .

JOURNAL OF CHEMICAL PHYSICS, 1958, 28 (02) :258-267

[7] Fast and stable explicit operator splitting methods for phase-field models [J].

Cheng, Yuanzhen ;

Kurganov, Alexander ;

Qu, Zhuolin ;

Tang, Tao .

JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 303 :45-65

[8] NUMERICAL-STUDIES OF THE CAHN-HILLIARD EQUATION FOR PHASE-SEPARATION [J].

ELLIOTT, CM ;

FRENCH, DA .

IMA JOURNAL OF APPLIED MATHEMATICS, 1987, 38 (02) :97-128

[9] THE GLOBAL DYNAMICS OF DISCRETE SEMILINEAR PARABOLIC EQUATIONS [J].

ELLIOTT, CM ;

STUART, AM .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1993, 30 (06) :1622-1663

[10] Unconditionally gradient stable time marching the Cahn-Hilliard equation [J].

Eyre, DJ .

COMPUTATIONAL AND MATHEMATICAL MODELS OF MICROSTRUCTURAL EVOLUTION, 1998, 529 :39-46

← 1 2 3 →