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Author:

Xu, Fei (Xu, Fei.) | Huang, Qiumei (Huang, Qiumei.) (Scholars:黄秋梅) | Yang, Huiting (Yang, Huiting.) | Ma, Hongkun (Ma, Hongkun.)

Indexed by:

EI Scopus SCIE

Abstract:

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.

Keyword:

Adaptive finite element method Multilevel correction method Convergence Goal-oriented

Author Community:

  • [ 1 ] [Xu, Fei]Beijing Univ Technol, Fac Sci, Beijing Inst Sci & Engn Comp, Beijing 100124, Peoples R China
  • [ 2 ] [Huang, Qiumei]Beijing Univ Technol, Fac Sci, Beijing Inst Sci & Engn Comp, Beijing 100124, Peoples R China
  • [ 3 ] [Yang, Huiting]Beijing Univ Technol, Fac Sci, Beijing Inst Sci & Engn Comp, Beijing 100124, Peoples R China
  • [ 4 ] [Ma, Hongkun]Zhuhai Huafa Investment Holdings Grp Co Ltd, Hengqin 519000, Peoples R China
  • [ 5 ] [Ma, Hongkun]Sun Yat Sen Univ, Business Sch, Guangzhou 510275, Peoples R China

Reprint Author's Address:

  • [Ma, Hongkun]Zhuhai Huafa Investment Holdings Grp Co Ltd, Hengqin 519000, Peoples R China

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Source :

APPLIED NUMERICAL MATHEMATICS

ISSN: 0168-9274

Year: 2022

Volume: 172

Page: 224-241

2 . 8

JCR@2022

2 . 8 0 0

JCR@2022

ESI Discipline: MATHEMATICS;

ESI HC Threshold:20

JCR Journal Grade:1

CAS Journal Grade:2

Cited Count:

WoS CC Cited Count: 4

SCOPUS Cited Count: 4

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 7

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