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 Decoupled Mixed Element Methods for Fourth Order Elliptic Optimal Control Problems with Control Constraints Shen, Yue1,2,3; Jin, Chang2,3 2020-05-01 Source Publication NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS ISSN 1004-8979 Volume 13Issue:2Pages:400-432 Abstract In this paper, we study the finite element methods for distributed optimal control problems governed by the biharmonic operator. Motivated from reducing the regularity of solution space, we use the decoupled mixed element method which was used to approximate the solution of biharmonic equation to solve the fourth order optimal control problems. Two finite element schemes, i.e., Lagrange conforming element combined with full control discretization and the nonconforming Crouzeix-Raviart element combined with variational control discretization, are used to discretize the decoupled optimal control system. The corresponding a priori error estimates are derived under appropriate norms which are then verified by extensive numerical experiments. Keyword Fourth order elliptic equation optimal control problem decoupled mixed element method Lagrange element nonconforming Crouzeix-Raviart element a priori error estimates DOI 10.4208/nmtma.OA-2019-0016 Indexed By SCI Language 英语 WOS Research Area Mathematics WOS Subject Mathematics, Applied ; Mathematics WOS ID WOS:000519598500007 Publisher GLOBAL SCIENCE PRESS Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/50911 Collection 中国科学院数学与系统科学研究院 Corresponding Author Shen, Yue Affiliation 1.Xian Univ Architecture & Technol, Xian 710055, Shaanxi, Peoples R China2.Univ Chinese Acad Sci, Beijing 100190, Peoples R China3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100190, Peoples R China Recommended CitationGB/T 7714 Shen, Yue,Jin, Chang. Decoupled Mixed Element Methods for Fourth Order Elliptic Optimal Control Problems with Control Constraints[J]. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,2020,13(2):400-432. APA Shen, Yue,&Jin, Chang.(2020).Decoupled Mixed Element Methods for Fourth Order Elliptic Optimal Control Problems with Control Constraints.NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,13(2),400-432. MLA Shen, Yue,et al."Decoupled Mixed Element Methods for Fourth Order Elliptic Optimal Control Problems with Control Constraints".NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS 13.2(2020):400-432.
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