New expansions of numerical eigenvalues for  by nonconforming elements |
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| Authors: | Qun Lin Hung-Tsai Huang Zi-Cai Li. |
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| Affiliation: | 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, Taiwan 840 ; (Corresponding author) Department of Applied Mathematics, and Department of Computer Science and Engineering, National Sun Yat-sen University, Kaohsiung, Taiwan 80424 |
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| Abstract: | The paper explores new expansions of the eigenvalues for  in  with Dirichlet boundary conditions by the bilinear element (denoted  ) and three nonconforming elements, the rotated bilinear element (denoted  ), the extension of  (denoted  ) and Wilson's elements. The expansions indicate that  and  provide upper bounds of the eigenvalues, and that  and Wilson's elements provide lower bounds of the eigenvalues. By extrapolation, the  convergence rate can be obtained, where  is the maximal boundary length of uniform rectangles. Numerical experiments are carried out to verify the theoretical analysis made. |
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| Keywords: | Bilinear elements rotated bilinear element the extension of rotated bilinear element Wilson's element eigenvalue problem extrapolation global superconvergence. |
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