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

被引：27

作者：

Li, Congying ^{[1
,3
]}

Huang, Yunqing ^{[2
]}

Yi, Nianyu ^{[1
]}

机构：

[1] Xiangtan Univ, Sch Math & Computat Sci, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Hunan, Peoples R China

[2] Xiangtan Univ, Sch Math & Computat Sci, Minist Educ, Key Lab Intelligent Comp & Informat Proc, Xiangtan 411105, Hunan, Peoples R China

[3] Huaihua Univ, Sch Math & Computat Sci, Huaihua 418000, Hunan, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2019年 / 353卷

关键词：

Allen-Cahn equation; Finite element method; Energy stable; Error estimation; IMAGE SEGMENTATION; NUMERICAL-ANALYSIS; MEAN-CURVATURE; COMPUTER-SIMULATION; CONTINUUM MODEL; GROWTH; APPROXIMATIONS; DYNAMICS; MOTION;

D O I：

10.1016/j.cam.2018.12.024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we design, analyze and numerically validate an unconditionally energy stable second order numerical method for solving the Allen-Cahn equation which represents a model for anti-phase domain coarsening in a binary alloy. The proposed scheme inherits the property of the decrease of the total energy from the Allen-Cahn equation. An error estimate for the fully discretized scheme is also established. Numerical examples are presented to confirm the accuracy, efficiency, and stability of the proposed method. In particular, the method is shown to be unconditionally energy stable and second order accurate in both time and space discretizations. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：38 / 48

页数：11

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