Multilevel correction goal-oriented adaptive finite element method for semilinear elliptic equations

被引：3
|
作者：
Xu, Fei [1 ]
Huang, Qiumei [1 ]
Yang, Huiting [1 ]
Ma, Hongkun [2 ,3 ]
机构：
[1] Beijing Univ Technol, Fac Sci, Beijing Inst Sci & Engn Comp, Beijing 100124, Peoples R China
[2] Zhuhai Huafa Investment Holdings Grp Co Ltd, Hengqin 519000, Peoples R China
[3] Sun Yat Sen Univ, Business Sch, Guangzhou 510275, Peoples R China
来源：
APPLIED NUMERICAL MATHEMATICS | 2022年 / 172卷
基金：
中国国家自然科学基金;
关键词：
Adaptive finite element method; Goal-oriented; Multilevel correction method; Convergence; POSTERIORI ERROR ESTIMATION; CAHN-HILLIARD; CONVERGENCE; SCHEME; ALGORITHM;
D O I：
10.1016/j.apnum.2021.10.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this study, a multilevel correction-type goal-oriented adaptive finite element method is designed for semilinear elliptic equations. Concurrently, the corresponding convergence property is theoretically proved. In the novel goal-oriented adaptive finite element method, only a linearized primal equation and a linearized dual equation are required to be solved in each adaptive finite element space. To ensure convergence, the approximate solution of the primal equation was corrected by solving a small-scale semilinear elliptic equation after the central solving process in each adaptive finite element space. Since solving of the large-scale semilinear elliptic equations is avoided and the goal-oriented technique is absorbed, there has been a significant improvement in the solving efficiency for the goal functional of semilinear elliptic equations. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：224 / 241
页数：18
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