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
相关论文
共 50 条
  • [31] Online basis construction for goal-oriented adaptivity in the generalized multiscale finite element method
    Chung, Eric
    Pollock, Sara
    Pun, Sai-Mang
    JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 393 : 59 - 73
  • [32] 3D MCSEM parallel goal-oriented adaptive vector finite element modeling
    Zhao Ning
    Wang XuBen
    Yu Gang
    He ZhanXiang
    Sun WeiBin
    Qin Ce
    CHINESE JOURNAL OF GEOPHYSICS-CHINESE EDITION, 2019, 62 (02): : 779 - 788
  • [33] Adaptive thermo-mechanical finite element formulation based on goal-oriented error estimation
    Rabizadeh, E.
    Bagherzadeh, A. Saboor
    Rabczuk, T.
    COMPUTATIONAL MATERIALS SCIENCE, 2015, 102 : 27 - 44
  • [34] DUAL-WEIGHTED GOAL-ORIENTED ADAPTIVE FINITE ELEMENTS FOR OPTIMAL CONTROL OF ELLIPTIC VARIATIONAL INEQUALITIES*
    Hintermueller, M.
    Hoppe, R. H. W.
    Loebhard, C.
    ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2014, 20 (02) : 524 - 546
  • [35] Goal-Oriented Regional Angular Adaptive Algorithm for the SN Equations
    Zhang, Bin
    Zhang, Liang
    Liu, Cong
    Chen, Yixue
    NUCLEAR SCIENCE AND ENGINEERING, 2018, 189 (02) : 120 - 134
  • [36] A self-adaptive goal-oriented hp finite element method with electromagnetic applications.: Part II:: Electrodynamics
    Pardo, D.
    Demkowicz, L.
    Torres-Verdin, C.
    Paszynski, M.
    COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2007, 196 (37-40) : 3585 - 3597
  • [37] Goal-Oriented Anisotropic hp-Adaptive Discontinuous Galerkin Method for the Euler Equations
    Dolejsi, Vit
    Roskovec, Filip
    COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION, 2022, 4 (01) : 143 - 179
  • [38] Goal-Oriented Anisotropic hp-Adaptive Discontinuous Galerkin Method for the Euler Equations
    Vít Dolejší
    Filip Roskovec
    Communications on Applied Mathematics and Computation, 2022, 4 : 143 - 179
  • [39] Goal-oriented error estimation based on equilibrated-flux reconstruction for finite element approximations of elliptic problems
    Mozolevski, Igor
    Prudhomme, Serge
    COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2015, 288 : 127 - 145
  • [40] A two-grid stabilized mixed finite element method for semilinear elliptic equations
    Weng, Zhifeng
    Feng, Xinlong
    Liu, Demin
    APPLIED MATHEMATICAL MODELLING, 2013, 37 (10-11) : 7037 - 7046
12345