Energy stable numerical schemes for the fractional-in-space Cahn-Hilliard equation

被引：12

作者：

Bu, Linlin ^{[1
]}

Mei, Liquan ^{[1
]}

Wang, Ying ^{[2
]}

Hou, Yan ^{[3
]}

机构：

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

[2] Xian Univ Architecture & Technol, Sch Sci, Xian 710055, Shaanxi, Peoples R China

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

来源：

APPLIED NUMERICAL MATHEMATICS | 2020年 / 158卷

关键词：

Fractional Cahn-Hilliard equation; Uniquely solvable; Mass conservative; Energy stable; Error estimates; FINITE-DIFFERENCE SCHEME; ALLEN-CAHN; 2ND-ORDER; APPROXIMATIONS;

D O I：

10.1016/j.apnum.2020.08.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a number of energy stable numerical schemes are proposed for the fractional Cahn-Hilliard equation. We prove mass conservation, unique solvability and energy stability for three time semi-discretized schemes based on the first-order semi-implicit scheme, the Crank-Nicolson scheme and the BDF2 scheme respectively. Then we present error analysis for these numerical schemes with the Fourier spectral approximation in space. Some numerical experiments are finally carried out to confirm accuracy and effectiveness of these proposed methods. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：392 / 414

页数：23

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