KMS Of Academy of mathematics and systems sciences, CAS
| ANALYSIS AND APPROXIMATIONS OF DIRICHLET BOUNDARY CONTROL OF STOKES FLOWS IN THE ENERGY SPACE | |
| Gong, Wei1,2; Mateos, Mariano3; Singler, John4; Zhang, Yangwen5 | |
| 2022 | |
| Source Publication | SIAM JOURNAL ON NUMERICAL ANALYSIS
 |
| ISSN | 0036-1429 |
| Volume | 60Issue:1Pages:450-474 |
| Abstract | 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. |
| Keyword | Dirichlet boundary control Stokes flows energy space regularity finite element method error estimates |
| DOI | 10.1137/21M1406799 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000765864500018 |
| Publisher | SIAM PUBLICATIONS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/60188 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Gong, Wei |
| Affiliation | 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 |
| Recommended Citation 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. |
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