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	Constructing both lower and upper bounds for the eigenvalues of elliptic operators by nonconforming finite element methods
	Hu, Jun ; Huang, Yunqing ; Shen, Quan
	2015
关键词	ERROR APPROXIMATION
英文摘要	This paper introduces a method of constructing nonconforming finite elements which can produce lower bounds for the eigenvalues of elliptic operators. Based on such nonconforming discrete eigenfunctions, we propose a simple method to produce upper bounds of eigenvalues. More precisely, we construct conforming approximations of exact eigenfunctions by a projection average interpolation operator of nonconforming discrete eigenfunctions. After showing the approximation property of the projection average interpolation operator, we prove that the Rayleigh quotients of the aforementioned conforming approximations are convergent to the exact eigenvalues from above. Finally, we combine lower and upper bounds of eigenvalues to obtain high accuracy approximations of eigenvalues. Numerical examples verify our theoretical results.; NSFC [11271035, 11421101, 91430213, 11401416]; International Science and Technology Cooperation Program of China [2010DFR00700]; SCI(E); ARTICLE; hujun@math.pku.edu.cn; huangyq@xtu.edu.cn; goodytiger@hotmail.com; 2; 273-302; 131
语种	英语
出处	SCI
出版者	NUMERISCHE MATHEMATIK
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/416075]
专题	数学科学学院
推荐引用方式 GB/T 7714	Hu, Jun,Huang, Yunqing,Shen, Quan. Constructing both lower and upper bounds for the eigenvalues of elliptic operators by nonconforming finite element methods. 2015-01-01.

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