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

文献类型：期刊论文

作者Gong, Wei4,5; Mateos, Mariano3; Singler, John2; Zhang, Yangwen1
刊名SIAM JOURNAL ON NUMERICAL ANALYSIS
出版日期2022
卷号60期号:1页码:450-474
关键词Dirichlet boundary control Stokes flows energy space regularity finite element method error estimates
ISSN号0036-1429
DOI10.1137/21M1406799
英文摘要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.
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
语种英语
WOS记录号WOS:000765864500018
出版者SIAM PUBLICATIONS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/60187]  
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.Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA
2.Missouri Univ Sci & Technol, Dept Math & Stat, Rolla, MO 65409 USA
3.Univ Oviedo, Dept Matemat, Campus Gijon, Gijon 33203, Spain
4.Chinese Acad Sci, Acad Math & Syst Sci, Natl Ctr Math & Interdisciplinary Sci, Beijing 100190, Peoples R China
5.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, Inst Computat Math, Beijing 100190, Peoples R China
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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