Multiscale asymptotic analysis and computations for Steklov eigenvalue problem in periodically perforated domain

doi:10.1002/mma.7565

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	Multiscale asymptotic analysis and computations for Steklov eigenvalue problem in periodically perforated domain
	Ye, Shuyu 1; Ma, Qiang 1; Hu, Bing 1; Cui, Junzhi 2; Jiang, Xue 3
	2021-06-19
发表期刊	MATHEMATICAL METHODS IN THE APPLIED SCIENCES
ISSN	0170-4214
页码	21
摘要	A second-order asymptotic analysis method is developed for the Steklov eigenvalue problem in periodically perforated domain. By the two-scale expansions of the eigenfunctions and eigenvalues, the first- and second-order cell functions defined on the representative cell are obtained successively, the homogenized elliptic eigenvalue problem is formulated, and effective coefficients are derived. The first- and second-order correctors of the eigenvalues are expressed in terms of the integrations of the cell functions and homogenized eigenfunctions. The error estimations of the expansions of eigenvalues are established, and the corresponding finite element algorithm is proposed. Numerical examples are carried out, and both qualitative and quantitative comparisons with the solutions by classical finite element computations are performed. It is demonstrated that this asymptotic model is effective to capture the local details of the eigenfunctions by considering the second-order expansion terms, and the algorithm presented in this work is efficient to obtain the accurate spectral properties of the porous material at lower cost.
关键词	corrector equations error estimation finite element computation second-order two-scale asymptotic analysis Steklov eigenvalue problem
DOI	10.1002/mma.7565
收录类别	SCI
语种	英语
资助项目	State Key Laboratory of Science and Engineering Computing ; Fundamental Research Funds for the Central Universities[YJ201811] ; National Natural Science Foundation of China[11671052] ; National Natural Science Foundation of China[11701123] ; National Natural Science Foundation of China[11771057] ; National Natural Science Foundation of China[11801387] ; National Natural Science Foundation of China[11971336] ; National Natural Science Foundation of China[11971337]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000663282000001
出版者	WILEY
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58819
专题	中国科学院数学与系统科学研究院
通讯作者	Ma, Qiang
作者单位	1.Sichuan Univ, Coll Math, 24 South Sect 1,Yihuan Rd, Chengdu 610065, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing, Peoples R China 3.Beijing Univ Technol, Coll Appl Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Ye, Shuyu,Ma, Qiang,Hu, Bing,et al. Multiscale asymptotic analysis and computations for Steklov eigenvalue problem in periodically perforated domain[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES,2021:21.
APA	Ye, Shuyu,Ma, Qiang,Hu, Bing,Cui, Junzhi,&Jiang, Xue.(2021).Multiscale asymptotic analysis and computations for Steklov eigenvalue problem in periodically perforated domain.MATHEMATICAL METHODS IN THE APPLIED SCIENCES,21.
MLA	Ye, Shuyu,et al."Multiscale asymptotic analysis and computations for Steklov eigenvalue problem in periodically perforated domain".MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2021):21.