New expansions of numerical eigenvalues by Wilson's element

Authors:
Qun Lin;Hung-Tsai Huang;Zi-Cai Li
Affiliations:
Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, P.O. Box 2719, Beijing 1000080, China;Department of Applied Mathematics, I-Shou University, 840, Taiwan;Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan and Department of Computer Science and Engineering, National Sun Yat-sen University, Kaohsiung, 80424, ...
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 5
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Abstract

The paper explores new expansions of eigenvalues for -@Du=@l@ru in S with Dirichlet boundary conditions by Wilson's element. The expansions indicate that Wilson's element provides lower bounds of the eigenvalues. By the extrapolation or the splitting extrapolation, the O(h^4) convergence rate can be obtained, where h is the maximal boundary length of uniform rectangles. Numerical experiments are carried to verify the theoretical analysis made. It is worth pointing out that these results are new, compared with the recent book, Lin and Lin [Q. Lin, J. Lin, Finite Element Methods; Accuracy and Improvement, Science Press, Beijing, 2006].