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

Linlin Bu; Liquan Mei; Yan Hou

doi:10.1016/j.camwa.2019.05.016

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

Linlin Bu
, Liquan Mei
, Yan Hou

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	3485-3500
Number of pages	16
Journal	Computers and Mathematics with Applications
Volume	78
Issue number	11
DOIs	https://doi.org/10.1016/j.camwa.2019.05.016
State	Published - 1 Dec 2019

Keywords

Convex splitting
Energy stable
Fractional Allen–Cahn equation
Fractional Cahn–Hilliard equation
Mass conservative
The unique solvability

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10.1016/j.camwa.2019.05.016

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title = "Stable second-order schemes for the space-fractional Cahn–Hilliard and Allen–Cahn equations",

abstract = "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.",

keywords = "Convex splitting, Energy stable, Fractional Allen–Cahn equation, Fractional Cahn–Hilliard equation, Mass conservative, The unique solvability",

author = "Linlin Bu and Liquan Mei and Yan Hou",

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T1 - Stable second-order schemes for the space-fractional Cahn–Hilliard and Allen–Cahn equations

AU - Bu, Linlin

AU - Mei, Liquan

AU - Hou, Yan

PY - 2019/12/1

Y1 - 2019/12/1

N2 - 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.

AB - 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.

KW - Convex splitting

KW - Energy stable

KW - Fractional Allen–Cahn equation

KW - Fractional Cahn–Hilliard equation

KW - Mass conservative

KW - The unique solvability

UR - https://www.scopus.com/pages/publications/85066447509

U2 - 10.1016/j.camwa.2019.05.016

DO - 10.1016/j.camwa.2019.05.016

M3 - 文章

AN - SCOPUS:85066447509

SN - 0898-1221

VL - 78

SP - 3485

EP - 3500

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 11

ER -

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

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Keywords

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