A High Accuracy Nonconforming Finite Element Scheme for Helmholtz Transmission Eigenvalue Problem

doi:10.1007/s10915-020-01247-4

	A High Accuracy Nonconforming Finite Element Scheme for Helmholtz Transmission Eigenvalue Problem
	Xi, Yingxia 2; Ji, Xia 1,3; Zhang, Shuo 4
刊名	JOURNAL OF SCIENTIFIC COMPUTING
	2020-06-15
卷号	83 期号:3 页码:20
关键词	Nonconforming finite element method Transmission eigenvalues High accurary
ISSN号	0885-7474
DOI	10.1007/s10915-020-01247-4
英文摘要	In this paper, we consider a cubic H-2 nonconforming finite element scheme B-h0(3) which does not correspond to a locally defined finite element with Ciarlet's triple but admit a set of local basis functions. For the first time, we deduce and write out the expression of basis functions explicitly. Distinguished from the most nonconforming finite element methods, (delta Delta(h)., Delta(h).) with non-constant coefficient delta > 0 is coercive on the nonconforming B-h0(3) space which makes it robust for numerical discretization. For fourth order eigenvalue problem, the B-h0(3) scheme can provide O(h(2)) approximation for the eigenspace in energy norm and O(h(4)) approximation for the eigenvalues. We test the B-h0(3) scheme on the vary-coefficient bi-Laplace source and eigenvalue problem, further, transmission eigenvalue problem. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed scheme.
资助项目	National Natural Science Foundation of China[11901295] ; National Natural Science Foundation of China[11971468] ; National Natural Science Foundation of China[91630313] ; National Natural Science Foundation of China[11471026] ; National Natural Science Foundation of China[11871465] ; Natural Science Foundation of Jiangsu Province[BK20190431] ; Start-up Fund for Scientific Research, Nanjing University of Science and Technology[AE89991/109] ; National Centre for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER/PLENUM PUBLISHERS
WOS记录号	WOS:000544999500002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/51735]
专题	中国科学院数学与系统科学研究院
通讯作者	Ji, Xia
作者单位	1.Beijing Inst Technol, Beijing Key Lab MCAACI, Beijing 100081, Peoples R China 2.Nanjing Univ Sci & Technol, Sch Sci, Nanjing 210094, Peoples R China 3.Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Xi, Yingxia,Ji, Xia,Zhang, Shuo. A High Accuracy Nonconforming Finite Element Scheme for Helmholtz Transmission Eigenvalue Problem[J]. JOURNAL OF SCIENTIFIC COMPUTING,2020,83(3):20.
APA	Xi, Yingxia,Ji, Xia,&Zhang, Shuo.(2020).A High Accuracy Nonconforming Finite Element Scheme for Helmholtz Transmission Eigenvalue Problem.JOURNAL OF SCIENTIFIC COMPUTING,83(3),20.
MLA	Xi, Yingxia,et al."A High Accuracy Nonconforming Finite Element Scheme for Helmholtz Transmission Eigenvalue Problem".JOURNAL OF SCIENTIFIC COMPUTING 83.3(2020):20.