The adaptive SAV weak Galerkin finite element method for the Allen-Cahn equation

被引：1
|
作者：
Liu, Ying [1 ]
Shen, Xiaoqin [1 ]
Guan, Zhen [2 ]
Nie, Yufeng [3 ]
机构：
[1] Xian Univ Technol, Sch Sci, Dept Math, Xian 710048, Shaanxi, Peoples R China
[2] Pingdingshan Univ, Sch Math & Stat, Pingdingshan 467000, Henan, Peoples R China
[3] Northwestern Polytech Univ, Sch Math & Stat, Xian 710129, Shaanxi, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2023年 / 151卷
关键词：
Weak Galerkin finite element method; SAV approach; Elliptic reconstruction; Adaptive algorithm; POLYNOMIAL PRESERVING RECOVERY; POSTERIORI ERROR CONTROL; PHASE-FIELD MODEL; ELLIPTIC RECONSTRUCTION; IMAGE SEGMENTATION; 2ND-ORDER; GRADIENT; APPROXIMATION; SUPERCONVERGENCE; ALGORITHM;
D O I：
10.1016/j.camwa.2023.10.023
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the weak Galerkin finite element method with the scalar auxiliary variable (SAV) approach is considered for the Allen-Cahn equation. Based on the elliptic reconstruction technique, the elliptic equation corresponding to the Allen-Cahn equation is introduced, which is employed to split the numerical error into the elliptic error and the parabolic error. Then the weak gradient recovery type a posteriori error estimator of the elliptic equation is adopted to develop the time-space adaptive algorithm. The effectiveness of the SAV weak Galerkin finite element method and the time-space adaptive algorithm is verified by several numerical benchmarks on both uniform and adaptive meshes.
引用
收藏
页码：449 / 460
页数：12
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