ANALYSIS AND APPROXIMATIONS OF DIRICHLET BOUNDARY CONTROL OF STOKES FLOWS IN THE ENERGY SPACE

doi:10.1137/21M1406799

CSpace

	ANALYSIS AND APPROXIMATIONS OF DIRICHLET BOUNDARY CONTROL OF STOKES FLOWS IN THE ENERGY SPACE
	Gong, Wei 1,2; Mateos, Mariano 3; Singler, John 4; Zhang, Yangwen 5
	2022
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	60 期号:1 页码:450-474
摘要	We study Dirichlet boundary control of Stokes flows in 2D polygonal domains. We consider cost functionals with two different boundary control regularization terms: the L-2(Gamma)-norm and an energy space seminorm. We prove well-posedness, provide first order optimality conditions, derive regularity results, and develop finite element discretizations for both problems, and we also prove finite element error estimates for the latter problem. The motivation to study the energy space problem follows from our analysis: we prove that the choice of the control space L-2(Gamma) can lead to an optimal control with discontinuities at the corners, even when the domain is convex. This phenomenon is also observed in numerical experiments. This behavior does not occur in Dirichlet boundary control problems for the Poisson equation on convex polygonal domains, and it may not be desirable in real applications. For the energy space problem, we show that the solution of the control problem is more regular than the solution of the problem with the L-2(Gamma)-regularization. The improved regularity enables us to prove a priori error estimates for the control in the energy norm. We present several numerical experiments for both control problems on convex and nonconvex domains.
关键词	Dirichlet boundary control Stokes flows energy space regularity finite element method error estimates
DOI	10.1137/21M1406799
收录类别	SCI
语种	英语
资助项目	Chinese Academy of Sciences[XDB 41000000] ; National Key Basic Research Program[2018YFB0704304] ; National Natural Science Foundation of China[11671391] ; National Natural Science Foundation of China[12071468] ; Spanish Ministerio de Economia y Competitividad[MTM2017-83185-P] ; National Science Foundation (NSF)[DMS-1818867]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000765864500018
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60188
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.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, Inst Computat Math, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Natl Ctr Math & Interdisciplinary Sci, Beijing 100190, Peoples R China 3.Univ Oviedo, Dept Matemat, Campus Gijon, Gijon 33203, Spain 4.Missouri Univ Sci & Technol, Dept Math & Stat, Rolla, MO 65409 USA 5.Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA
推荐引用方式 GB/T 7714	Gong, Wei,Mateos, Mariano,Singler, John,et al. ANALYSIS AND APPROXIMATIONS OF DIRICHLET BOUNDARY CONTROL OF STOKES FLOWS IN THE ENERGY SPACE[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2022,60(1):450-474.
APA	Gong, Wei,Mateos, Mariano,Singler, John,&Zhang, Yangwen.(2022).ANALYSIS AND APPROXIMATIONS OF DIRICHLET BOUNDARY CONTROL OF STOKES FLOWS IN THE ENERGY SPACE.SIAM JOURNAL ON NUMERICAL ANALYSIS,60(1),450-474.
MLA	Gong, Wei,et al."ANALYSIS AND APPROXIMATIONS OF DIRICHLET BOUNDARY CONTROL OF STOKES FLOWS IN THE ENERGY SPACE".SIAM JOURNAL ON NUMERICAL ANALYSIS 60.1(2022):450-474.