A SCR-based error estimation and adaptive finite element method for the Allen-Cahn equation

被引：33

作者：

Chen, Yaoyao ^{[1
]}

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

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2019年 / 78卷 / 01期

关键词：

Allen-Cahn equation; Superconvergent cluster recovery; A posteriori error estimation; Adaptive; Finite element method; COMPUTER-SIMULATION; IMAGE SEGMENTATION; NUMERICAL-ANALYSIS; CONTINUUM MODEL; GROWTH; RECOVERY; APPROXIMATIONS; DYNAMICS;

D O I：

10.1016/j.camwa.2019.02.022

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the adaptive finite element method for the Allen-Cahn equation. The adaptive method is based on a second order accurate unconditionally energy stable finite element scheme and a recovery-type a posteriori error estimator. A SCR-based a posteriori error estimation is derived to control the mesh refinement and coarsening. A time-space adaptive algorithm is proposed for numerical approximation of the Allen-Cahn equation. Numerical experiments are presented to illustrate the reliability and efficiency of the proposed SCR-based error estimator and the corresponding adaptive algorithm. The extension of the proposed adaptive algorithm to the Cahn-Hilliard equation is also discussed. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页码：204 / 223

页数：20

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