A MULTILEVEL CORRECTION TYPE OF ADAPTIVE FINITE ELEMENT METHOD FOR EIGENVALUE PROBLEMS

doi:10.1137/17M1138157

	A MULTILEVEL CORRECTION TYPE OF ADAPTIVE FINITE ELEMENT METHOD FOR EIGENVALUE PROBLEMS
	Hong, Qichen 1,2; Xie, Hehu1,2 ; Xu, Fei 3
	2018
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	40 期号:6 页码:A4208-A4235
摘要	An adaptive finite element method for eigenvalue problems is proposed based on the multilevel correction scheme. Different from the standard adaptive finite element method which requires solving eigenvalue problems on adaptively refined triangulations, our scheme only includes solving associated boundary value problems on adaptive triangulations and small scale eigenvalue problems on a very low dimensional space. Since there is no eigenvalue problem to be solved on adaptively refined triangulations, which needs more computation and memory than solving associated boundary value problem, the efficiency of the proposed method can be improved to be similar to that of the adaptive finite element method for associated boundary value problems. The convergence and optimal complexity is theoretically verified and numerically demonstrated.
关键词	eigenvalue problem multilevel correction adaptive finite element method convergence optimal complexity
DOI	10.1137/17M1138157
语种	英语
资助项目	Science Challenge Project[TZ2016002] ; National Natural Science Foundations of China[NSFC 11771434] ; National Natural Science Foundations of China[91330202] ; National Natural Science Foundations of China[11801021] ; National Natural Science Foundations of China[11371026] ; National Natural Science Foundations of China[11001259] ; National Center for Mathematics and Interdisciplinary Science, CAS
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000453747800022
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/31855
专题	计算数学与科学工程计算研究所
通讯作者	Hong, Qichen
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Beijing Univ Technol, Beijing Inst Sci & Engn Comp, Beijing 100124, Peoples R China
推荐引用方式 GB/T 7714	Hong, Qichen,Xie, Hehu,Xu, Fei. A MULTILEVEL CORRECTION TYPE OF ADAPTIVE FINITE ELEMENT METHOD FOR EIGENVALUE PROBLEMS[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2018,40(6):A4208-A4235.
APA	Hong, Qichen,Xie, Hehu,&Xu, Fei.(2018).A MULTILEVEL CORRECTION TYPE OF ADAPTIVE FINITE ELEMENT METHOD FOR EIGENVALUE PROBLEMS.SIAM JOURNAL ON SCIENTIFIC COMPUTING,40(6),A4208-A4235.
MLA	Hong, Qichen,et al."A MULTILEVEL CORRECTION TYPE OF ADAPTIVE FINITE ELEMENT METHOD FOR EIGENVALUE PROBLEMS".SIAM JOURNAL ON SCIENTIFIC COMPUTING 40.6(2018):A4208-A4235.