Multilevel correction goal-oriented adaptive finite element method for semilinear elliptic equations
被引:3
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作者:
Xu, Fei
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机构:
Beijing Univ Technol, Fac Sci, Beijing Inst Sci & Engn Comp, Beijing 100124, Peoples R ChinaBeijing Univ Technol, Fac Sci, Beijing Inst Sci & Engn Comp, Beijing 100124, Peoples R China
Xu, Fei
[1
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Huang, Qiumei
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机构:
Beijing Univ Technol, Fac Sci, Beijing Inst Sci & Engn Comp, Beijing 100124, Peoples R ChinaBeijing Univ Technol, Fac Sci, Beijing Inst Sci & Engn Comp, Beijing 100124, Peoples R China
Huang, Qiumei
[1
]
Yang, Huiting
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机构:
Beijing Univ Technol, Fac Sci, Beijing Inst Sci & Engn Comp, Beijing 100124, Peoples R ChinaBeijing Univ Technol, Fac Sci, Beijing Inst Sci & Engn Comp, Beijing 100124, Peoples R China
Yang, Huiting
[1
]
Ma, Hongkun
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机构:
Zhuhai Huafa Investment Holdings Grp Co Ltd, Hengqin 519000, Peoples R China
Sun Yat Sen Univ, Business Sch, Guangzhou 510275, Peoples R ChinaBeijing Univ Technol, Fac Sci, Beijing Inst Sci & Engn Comp, Beijing 100124, Peoples R China
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
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.
机构:
Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, NCMIS,LSEC, Beijing 100190, Peoples R ChinaChinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, NCMIS,LSEC, Beijing 100190, Peoples R China
Gong, Wei
Xie, Hehu
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机构:
Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, NCMIS,LSEC, Beijing 100190, Peoples R China
Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R ChinaChinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, NCMIS,LSEC, Beijing 100190, Peoples R China
Xie, Hehu
Yan, Ningning
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机构:
Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, NCMIS,LSEC, Beijing 100190, Peoples R ChinaChinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, NCMIS,LSEC, Beijing 100190, Peoples R China
机构:
Mansoura Univ, Fac Engn, Math & Engn Phys Dept, Mansoura, Egypt
German Int Univ GIU, Dept Math, Cairo, EgyptMansoura Univ, Fac Engn, Math & Engn Phys Dept, Mansoura, Egypt
机构:
Cent S Univ, Sch Geosci & Info Phys, Changsha 410083, Hunan, Peoples R ChinaCent S Univ, Sch Geosci & Info Phys, Changsha 410083, Hunan, Peoples R China
Ren, Zhengyong
Tang, Jingtian
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机构:
Cent S Univ, Sch Geosci & Info Phys, Changsha 410083, Hunan, Peoples R ChinaCent S Univ, Sch Geosci & Info Phys, Changsha 410083, Hunan, Peoples R China