Error Estimates for Finite Element Approximation of Dirichlet Boundary Control for Stokes Equations in L-2(Gamma)

doi:10.1007/s10915-022-01831-w

CSpace

	Error Estimates for Finite Element Approximation of Dirichlet Boundary Control for Stokes Equations in L-2(Gamma)
	Zhou, Kaiye 1,2; Gong, Wei 1,3
	2022-05-01
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING
ISSN	0885-7474
卷号	91 期号:2 页码:36
摘要	In this paper we study the finite element approximation of Dirichlet boundary control for Stokes equations in the control space L-2(Gamma). The governing state equation is understood in the very weak sense which ensures the well-posedness of the optimization problem. We consider the boundary control problems posed on either convex polygonal domains or smooth domains, and derive the respective regularity results for the solutions. A priori error estimates for the Taylor-Hood finite element approximation to the optimization problem are derived for the control variable for both classes of computational domains, where the smooth domain is approximated by a polygonal one. We obtain nearly half an order convergence for the control on convex polygonal domains that reflects the global regularity of the control, while in smooth domains we obtain first order convergence that is dominated by the geometric approximation error of the outward normal vector. Numerical experiments are presented to validate the theoretical results.
关键词	Dirichlet boundary control Stokes equations Polygonal/polyhedral domain Smooth domain Finite elements Error estimates
DOI	10.1007/s10915-022-01831-w
收录类别	SCI
语种	英语
资助项目	Strategic Priority Research Program of Chinese Academy of Sciences[XDB 41000000] ; National Key Basic Research Program[2018YFB0704304] ; National Natural Science Foundation of China[12071468] ; National Natural Science Foundation of China[11671391]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000776088200001
出版者	SPRINGER/PLENUM PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60231
专题	中国科学院数学与系统科学研究院
通讯作者	Gong, Wei
作者单位	1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC,NCMIS, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Zhou, Kaiye,Gong, Wei. Error Estimates for Finite Element Approximation of Dirichlet Boundary Control for Stokes Equations in L-2(Gamma)[J]. JOURNAL OF SCIENTIFIC COMPUTING,2022,91(2):36.
APA	Zhou, Kaiye,&Gong, Wei.(2022).Error Estimates for Finite Element Approximation of Dirichlet Boundary Control for Stokes Equations in L-2(Gamma).JOURNAL OF SCIENTIFIC COMPUTING,91(2),36.
MLA	Zhou, Kaiye,et al."Error Estimates for Finite Element Approximation of Dirichlet Boundary Control for Stokes Equations in L-2(Gamma)".JOURNAL OF SCIENTIFIC COMPUTING 91.2(2022):36.