Convergence of adaptive nonconforming finite element method for Stokes optimal control problems

doi:10.1016/j.cam.2022.114336

	Convergence of adaptive nonconforming finite element method for Stokes optimal control problems
	Shen, Yue 1; Gong, Wei 2; Yan, Ningning 3
刊名	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
	2022-10-01
卷号	412 页码:23
关键词	Optimal control problem Stokes equations Control constraints Adaptive nonconforming finite element method Convergence and quasi-optimality
ISSN号	0377-0427
DOI	10.1016/j.cam.2022.114336
英文摘要	This 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.
资助项目	Shaanxi 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研究方向	Mathematics
语种	英语
出版者	ELSEVIER
WOS记录号	WOS:000829826200017
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/61142]
专题	中国科学院数学与系统科学研究院
通讯作者	Shen, Yue
作者单位	1.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
推荐引用方式 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.