CSpace  > 系统科学研究所
HETEROGENEOUS MULTISCALE METHOD FOR OPTIMAL CONTROL PROBLEM GOVERNED BY ELLIPTIC EQUATIONS WITH HIGHLY OSCILLATORY COEFFICIENTS
Ge, Liang1; Yan, Ningning2; Wang, Lianhai3; Liu, Wenbin4; Yang, Danping5
2018
Source PublicationJOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN0254-9409
Volume36Issue:5Pages:644-660
AbstractIn this paper, we investigate heterogeneous multiscale method (HMM) for the optimal control problem with distributed control constraints governed by elliptic equations with highly oscillatory coefficients. The state variable and co-state variable are approximated by the multiscale discretization scheme that relies on coupled macro and micro finite elements, whereas the control variable is discretized by the piecewise constant. By applying the well-known Lions' Lemma to the discretized optimal control problem, we obtain the necessary and sufficient optimality conditions. A priori error estimates in both L-2 and H-1 norms are derived for the state, co-state and the control variable with uniform bound constants. Finally, numerical examples are presented to illustrate our theoretical results.
KeywordConstrained convex optimal control Heterogeneous multiscale finite element A priori error estimate Elliptic equations with highly oscillatory coefficients
DOI10.4208/jcm.1703-m2015-0433
Language英语
Funding ProjectShandong Province Outstanding Young Scientists Research Award Fund Project[BS2013DX010] ; Natural Science Foundation of Shandong Province, China[ZR2011FQ030] ; Natural Science Foundation of Shandong Province, China[ZR2013FQ001] ; Natural Science Foundation of Shandong Province, China[ZR2013FM025] ; Natural Science Foundation of China[11501326] ; Natural Science Foundation of China[11571356] ; Shandong Academy of Sciences Youth Fund Project[2013QN007]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000455996800002
PublisherGLOBAL SCIENCE PRESS
Citation statistics
Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/32227
Collection系统科学研究所
Affiliation1.Univ Jinan, Sch Math Sci, Jinan 250022, Shandong, Peoples R China
2.Chinese Acad Sci, Inst Syst Sci, Acad Math & Syst Sci, Beijing 10080, Peoples R China
3.Shandong Comp Sci Ctr, Shandong Prov Key Lab Comp Networks, Jinan 250014, Shandong, Peoples R China
4.Univ Kent, KBS, Canterbury CT2 7PE, Kent, England
5.East China Normal Univ, Dept Math, Shanghai 200062, Peoples R China
Recommended Citation
GB/T 7714
Ge, Liang,Yan, Ningning,Wang, Lianhai,et al. HETEROGENEOUS MULTISCALE METHOD FOR OPTIMAL CONTROL PROBLEM GOVERNED BY ELLIPTIC EQUATIONS WITH HIGHLY OSCILLATORY COEFFICIENTS[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2018,36(5):644-660.
APA Ge, Liang,Yan, Ningning,Wang, Lianhai,Liu, Wenbin,&Yang, Danping.(2018).HETEROGENEOUS MULTISCALE METHOD FOR OPTIMAL CONTROL PROBLEM GOVERNED BY ELLIPTIC EQUATIONS WITH HIGHLY OSCILLATORY COEFFICIENTS.JOURNAL OF COMPUTATIONAL MATHEMATICS,36(5),644-660.
MLA Ge, Liang,et al."HETEROGENEOUS MULTISCALE METHOD FOR OPTIMAL CONTROL PROBLEM GOVERNED BY ELLIPTIC EQUATIONS WITH HIGHLY OSCILLATORY COEFFICIENTS".JOURNAL OF COMPUTATIONAL MATHEMATICS 36.5(2018):644-660.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Ge, Liang]'s Articles
[Yan, Ningning]'s Articles
[Wang, Lianhai]'s Articles
Baidu academic
Similar articles in Baidu academic
[Ge, Liang]'s Articles
[Yan, Ningning]'s Articles
[Wang, Lianhai]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Ge, Liang]'s Articles
[Yan, Ningning]'s Articles
[Wang, Lianhai]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.
 

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.