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

doi:10.4208/jcm.1703-m2015-0433

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	HETEROGENEOUS MULTISCALE METHOD FOR OPTIMAL CONTROL PROBLEM GOVERNED BY ELLIPTIC EQUATIONS WITH HIGHLY OSCILLATORY COEFFICIENTS
	Ge, Liang 1; Yan, Ningning2 ; Wang, Lianhai 3; Liu, Wenbin 4; Yang, Danping 5
	2018
发表期刊	JOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN	0254-9409
卷号	36 期号:5 页码:644-660
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.
关键词	Constrained convex optimal control Heterogeneous multiscale finite element A priori error estimate Elliptic equations with highly oscillatory coefficients
DOI	10.4208/jcm.1703-m2015-0433
语种	英语
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
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000455996800002
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32227
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.