KMS Of Academy of mathematics and systems sciences, CAS
Optimal convergence of finite element approximation to an optimization problem with PDE constraint* | |
Gong, Wei1,2; Tan, Zhiyu3; Zhou, Zhaojie4 | |
2022-04-01 | |
Source Publication | INVERSE PROBLEMS |
ISSN | 0266-5611 |
Volume | 38Issue:4Pages:45 |
Abstract | We study in this paper the optimal convergence of finite element approximation to an optimization problem with PDE constraint. Specifically, we consider an elliptic distributed optimal control problem without control constraints, which can also be viewed as a regularized inverse source problem. The main contributions are two-fold. First, we derive a priori and a posteriori error estimates for the optimization problems, under an appropriately chosen norm that allows us to establish an isomorphism between the solution space and its dual. These results yield error estimates with explicit dependence on the regularization parameter alpha so that the constants appeared in the derivation are independent of alpha. Second, we prove the contraction property and rate optimality for the adaptive algorithm with respect to the error estimator and solution errors between the adaptive finite element solutions and the continuous solutions. Extensive numerical experiments are presented that confirm our theoretical results. |
Keyword | inverse source problem optimal control finite element method a priori error estimate a posteriori error estimate adaptivity rate optimality |
DOI | 10.1088/1361-6420/ac4f5c |
Indexed By | SCI |
Language | 英语 |
WOS Research Area | Mathematics ; Physics |
WOS Subject | Mathematics, Applied ; Physics, Mathematical |
WOS ID | WOS:000766855100001 |
Publisher | IOP Publishing Ltd |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/60104 |
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, NCMIS, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Inst Computat Math, Beijing 100190, Peoples R China 3.Louisiana State Univ, Ctr Computat & Technol, Baton Rouge, LA 70803 USA 4.Shandong Normal Univ, Sch Math & Stat, Jinan 250014, Peoples R China |
Recommended Citation GB/T 7714 | Gong, Wei,Tan, Zhiyu,Zhou, Zhaojie. Optimal convergence of finite element approximation to an optimization problem with PDE constraint*[J]. INVERSE PROBLEMS,2022,38(4):45. |
APA | Gong, Wei,Tan, Zhiyu,&Zhou, Zhaojie.(2022).Optimal convergence of finite element approximation to an optimization problem with PDE constraint*.INVERSE PROBLEMS,38(4),45. |
MLA | Gong, Wei,et al."Optimal convergence of finite element approximation to an optimization problem with PDE constraint*".INVERSE PROBLEMS 38.4(2022):45. |
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