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HETEROGENEOUS MULTISCALE METHOD FOR OPTIMAL CONTROL PROBLEM GOVERNED BY ELLIPTIC EQUATIONS WITH HIGHLY OSCILLATORY COEFFICIENTS

文献类型：期刊论文

作者Ge, Liang1; Yan, Ningning2; Wang, Lianhai3; Liu, Wenbin4; Yang, Danping5
刊名JOURNAL OF COMPUTATIONAL MATHEMATICS
出版日期2018
卷号36期号:5页码:644-660
关键词Constrained convex optimal control Heterogeneous multiscale finite element A priori error estimate Elliptic equations with highly oscillatory coefficients
ISSN号0254-9409
DOI10.4208/jcm.1703-m2015-0433
英文摘要In 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.
资助项目Shandong 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研究方向Mathematics
语种英语
WOS记录号WOS:000455996800002
出版者GLOBAL SCIENCE PRESS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/32226]  
专题系统科学研究所
通讯作者Ge, Liang
作者单位1.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
推荐引用方式
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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