Optimal convergence of finite element approximation to an optimization problem with PDE constraint*
文献类型：期刊论文
| 作者 | Gong, Wei3,4; Tan, Zhiyu2; Zhou, Zhaojie1 |
| 刊名 | INVERSE PROBLEMS
 |
| 出版日期 | 2022-04-01 |
| 卷号 | 38期号:4页码:45 |
| 关键词 | inverse source problem optimal control finite element method a priori error estimate a posteriori error estimate adaptivity rate optimality |
| ISSN号 | 0266-5611 |
| DOI | 10.1088/1361-6420/ac4f5c |
| 英文摘要 | 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. |
| WOS研究方向 | Mathematics ; Physics |
| 语种 | 英语 |
| WOS记录号 | WOS:000766855100001 |
| 出版者 | IOP Publishing Ltd |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/60103]  |
| 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.Shandong Normal Univ, Sch Math & Stat, Jinan 250014, Peoples R China 2.Louisiana State Univ, Ctr Computat & Technol, Baton Rouge, LA 70803 USA 3.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Inst Computat Math, Beijing 100190, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, Beijing 100190, Peoples R China |
| 推荐引用方式 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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