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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 PublicationNUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
ISSN1004-8979
Volume13Issue:2Pages:400-432
AbstractIn 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.
KeywordFourth order elliptic equation optimal control problem decoupled mixed element method Lagrange element nonconforming Crouzeix-Raviart element a priori error estimates
DOI10.4208/nmtma.OA-2019-0016
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000519598500007
PublisherGLOBAL SCIENCE PRESS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/50911
Collection中国科学院数学与系统科学研究院
Corresponding AuthorShen, Yue
Affiliation1.Xian Univ Architecture & Technol, Xian 710055, Shaanxi, Peoples R China
2.Univ Chinese Acad Sci, Beijing 100190, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
GB/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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