KMS Of Academy of mathematics and systems sciences, CAS
Error Estimates for Finite Element Approximation of Dirichlet Boundary Control for Stokes Equations in L-2(Gamma) | |
Zhou, Kaiye1,2; Gong, Wei1,3 | |
2022-05-01 | |
Source Publication | JOURNAL OF SCIENTIFIC COMPUTING |
ISSN | 0885-7474 |
Volume | 91Issue:2Pages:36 |
Abstract | 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. |
Keyword | Dirichlet boundary control Stokes equations Polygonal/polyhedral domain Smooth domain Finite elements Error estimates |
DOI | 10.1007/s10915-022-01831-w |
Indexed By | SCI |
Language | 英语 |
Funding Project | 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 Research Area | Mathematics |
WOS Subject | Mathematics, Applied |
WOS ID | WOS:000776088200001 |
Publisher | SPRINGER/PLENUM PUBLISHERS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/60231 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Gong, Wei |
Affiliation | 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 |
Recommended Citation 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. |
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