Analysis of the Fourier series Dirichlet-to-Neumann boundary condition of the Helmholtz equation and its application to finite element methods

doi:10.1007/s00211-021-01195-7

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	Analysis of the Fourier series Dirichlet-to-Neumann boundary condition of the Helmholtz equation and its application to finite element methods
	Xu, Liwei 1; Yin, Tao 2,3
	2021-03-25
发表期刊	NUMERISCHE MATHEMATIK
ISSN	0029-599X
页码	30
摘要	It is well known that the Fourier series Dirichlet-to-Neumann (DtN) boundary condition can be used to solve the Helmholtz equation in unbounded domains. In this work, applying such DtN boundary condition and using the finite element method, we analyze and solve a two dimensional transmission problem describing elastic waves inside a bounded and closed elastic obstacle and acoustic waves outside it. We are mainly interested in analyzing the DtN boundary condition of the Helmholtz equation in order to establish the well-posedness results of the approximated variational equation, and further derive a priori error estimates involving effects of both the finite element discretization and the truncation of DtN map. Finally, some numerical results are presented to illustrate the accuracy of the numerical scheme.
关键词	35J25 65N30 74F10
DOI	10.1007/s00211-021-01195-7
收录类别	SCI
语种	英语
资助项目	Key Project of the Major Research Plan of NSFC[91630205] ; NSFC[11771068] ; NSFC[12071060]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000632804400001
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58297
专题	中国科学院数学与系统科学研究院
通讯作者	Xu, Liwei
作者单位	1.Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Sichuan, Peoples R China 2.CALTECH, Dept Comp & Math Sci, 1200 East Calif Blvd, Pasadena, CA 91125 USA 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Xu, Liwei,Yin, Tao. Analysis of the Fourier series Dirichlet-to-Neumann boundary condition of the Helmholtz equation and its application to finite element methods[J]. NUMERISCHE MATHEMATIK,2021:30.
APA	Xu, Liwei,&Yin, Tao.(2021).Analysis of the Fourier series Dirichlet-to-Neumann boundary condition of the Helmholtz equation and its application to finite element methods.NUMERISCHE MATHEMATIK,30.
MLA	Xu, Liwei,et al."Analysis of the Fourier series Dirichlet-to-Neumann boundary condition of the Helmholtz equation and its application to finite element methods".NUMERISCHE MATHEMATIK (2021):30.