Optimal convergence of finite element approximation to an optimization problem with PDE constraint*                                 *                  Wei Gong was supported by the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB 41000000), the National Key Basic Research Program (Grant No. 2018YFB0704304) and the National Natural Science Foundation of China (Grant No. 12071468, 11671391). Zhaojie Zhou was supported by the National Natural Science Foundation of China under Grant No. 11971276.

doi:10.1088/1361-6420/ac4f5c

CSpace

	Optimal convergence of finite element approximation to an optimization problem with PDE constraint* * Wei Gong was supported by the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB 41000000), the National Key Basic Research Program (Grant No. 2018YFB0704304) and the National Natural Science Foundation of China (Grant No. 12071468, 11671391). Zhaojie Zhou was supported by the National Natural Science Foundation of China under Grant No. 11971276.
	Gong,Wei 1; Tan,Zhiyu 2; Zhou,Zhaojie 3
	2022-03-02
发表期刊	Inverse Problems
ISSN	0266-5611
卷号	38 期号:4
摘要	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 α so that the constants appeared in the derivation are independent of α. 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.
关键词	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
语种	英语
WOS记录号	IOP:ip_38_4_045004
出版者	IOP Publishing
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60082
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.NCMIS & LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China 2.Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803, United States of America 3.School of Mathematics and Statistics, Shandong Normal University, Ji’nan 250014, People’s Republic of 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* * Wei Gong was supported by the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB 41000000), the National Key Basic Research Program (Grant No. 2018YFB0704304) and the National Natural Science Foundation of China (Grant No. 12071468, 11671391). Zhaojie Zhou was supported by the National Natural Science Foundation of China under Grant No. 11971276.[J]. Inverse Problems,2022,38(4).
APA	Gong,Wei,Tan,Zhiyu,&Zhou,Zhaojie.(2022).Optimal convergence of finite element approximation to an optimization problem with PDE constraint* * Wei Gong was supported by the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB 41000000), the National Key Basic Research Program (Grant No. 2018YFB0704304) and the National Natural Science Foundation of China (Grant No. 12071468, 11671391). Zhaojie Zhou was supported by the National Natural Science Foundation of China under Grant No. 11971276..Inverse Problems,38(4).
MLA	Gong,Wei,et al."Optimal convergence of finite element approximation to an optimization problem with PDE constraint* * Wei Gong was supported by the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB 41000000), the National Key Basic Research Program (Grant No. 2018YFB0704304) and the National Natural Science Foundation of China (Grant No. 12071468, 11671391). Zhaojie Zhou was supported by the National Natural Science Foundation of China under Grant No. 11971276.".Inverse Problems 38.4(2022).