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Convergence of adaptive nonconforming finite element method for Stokes optimal control problems
Shen, Yue1; Gong, Wei2; Yan, Ningning3
2022-10-01
Source PublicationJOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN0377-0427
Volume412Pages:23
AbstractThis paper aims at proving the convergence and quasi-optimality of an adaptive nonconforming finite element method for Stokes distributed control problems with pointwise control constraints. Nonconforming P-1/P-0 pair (Crouzeix-Raviart elements) and variational discretization are used to approximate the state equation and the control variable, respectively. A posteriori error estimates with upper and lower bounds are first derived for the state and adjoint variables. Then we prove the contraction property for the sum of the energy error of the state and adjoint state and the scaled error estimator on two consecutive adaptive meshes. The resulting linear convergence is finally used to show the quasi-optimal convergence rate of the adaptive algorithm. Additionally, some numerical results are provided to support our theoretical analysis. (c) 2022 Elsevier B.V. All rights reserved.
KeywordOptimal control problem Stokes equations Control constraints Adaptive nonconforming finite element method Convergence and quasi-optimality
DOI10.1016/j.cam.2022.114336
Indexed BySCI
Language英语
Funding ProjectShaanxi Provincial Education Department, China[20JK0718] ; Natural Science Foundation of Shaanxi Province, China[2021JQ-492] ; National Natural Science Foundation of China[11571356] ; National Natural Science Foundation of China[91530204] ; National Natural Science Foundation of China[11671391]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000829826200017
PublisherELSEVIER
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/61143
Collection中国科学院数学与系统科学研究院
Corresponding AuthorShen, Yue
Affiliation1.Xian Univ Architecture & Technol, Sch Sci, Xian 710055, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC,NCMIS, Beijing 100190, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, LSEC,NCMIS, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Shen, Yue,Gong, Wei,Yan, Ningning. Convergence of adaptive nonconforming finite element method for Stokes optimal control problems[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2022,412:23.
APA Shen, Yue,Gong, Wei,&Yan, Ningning.(2022).Convergence of adaptive nonconforming finite element method for Stokes optimal control problems.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,412,23.
MLA Shen, Yue,et al."Convergence of adaptive nonconforming finite element method for Stokes optimal control problems".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 412(2022):23.
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