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	A High Accuracy Post-processing Algorithm for the Eigenvalues of Elliptic Operators
	Hu, Jun ; Huang, Yunqing ; Shen, Quan
	2012
关键词	Lower bound Upper bound Eigenvalue problem Nonconforming finite element Conforming finite element FINITE-ELEMENT APPROXIMATION EQUATIONS
英文摘要	In a very recent paper (Hu et al., The lower bounds for eigenvalues of elliptic operators by nonconforming finite element methods, Preprint, 2010), we prove that the eigenvalues by the nonconforming finite element methods are smaller than the exact ones for the elliptic operators. It is well-known that the conforming finite element methods produce the eigenvalues above to the exact ones. In this paper, we combine these two aspects and derive a new post-processing algorithm to approximate the eigenvalues of elliptic operators. We implement this algorithm and find that it actually yields very high accuracy approximation on very coarser mesh. The numerical results demonstrate that the high accuracy herein is of two fold: the much higher accuracy approximation on the very coarser mesh and the much higher convergence rate than a single lower/upper bound approximation. Moreover, we propose some acceleration technique for the algorithm of the discrete eigenvalue problem based on the solution of the discrete eigenvalue problem which yields the upper bound of the eigenvalue. With this acceleration technique we only need several iterations (two iterations in our example) to find the numerical solution of the discrete eigenvalue problem which produces the lower bound of the eigenvalue. Therefore we only need to solve essentially one discrete eigenvalue problem.; Mathematics, Applied; SCI(E); EI; 0; ARTICLE; 2; 426-445; 52
语种	英语
出处	EI ; SCI
出版者	journal of scientific computing
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/157531]
专题	数学科学学院
推荐引用方式 GB/T 7714	Hu, Jun,Huang, Yunqing,Shen, Quan. A High Accuracy Post-processing Algorithm for the Eigenvalues of Elliptic Operators. 2012-01-01.

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