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Volume 30, Issue 5
The Ultraconvergence of Eigenvalues for Bi-Quadratic Finite Elements

Lingxiong Meng & Zhimin Zhang

DOI: 10.4208/jcm.1203-m3977

J. Comp. Math., 30 (2012), pp. 555-564.

Published online: 2012-10

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  • Abstract

The classical eigenvalue problem of the second-order elliptic operator is approximated with bi-quadratic finite element in this paper. We construct a new superconvergent function recovery operator, from which the $O(h^8|\ln h|^2)$ ultraconvergence of eigenvalue approximation is obtained. Numerical experiments verify the theoretical results.

  • Keywords

Finite element method, Eigenvalue recovery, Ultraconvergence

  • AMS Subject Headings

65N30, 65N15, 65D10,74S05, 41A10, 41A25.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-30-555, author = {Lingxiong Meng and Zhimin Zhang}, title = {The Ultraconvergence of Eigenvalues for Bi-Quadratic Finite Elements}, journal = {Journal of Computational Mathematics}, year = {2012}, volume = {30}, number = {5}, pages = {555--564}, abstract = {

The classical eigenvalue problem of the second-order elliptic operator is approximated with bi-quadratic finite element in this paper. We construct a new superconvergent function recovery operator, from which the $O(h^8|\ln h|^2)$ ultraconvergence of eigenvalue approximation is obtained. Numerical experiments verify the theoretical results.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1203-m3977}, url = {http://global-sci.org/intro/article_detail/jcm/8450.html} }
TY - JOUR T1 - The Ultraconvergence of Eigenvalues for Bi-Quadratic Finite Elements AU - Lingxiong Meng & Zhimin Zhang JO - Journal of Computational Mathematics VL - 5 SP - 555 EP - 564 PY - 2012 DA - 2012/10 SN - 30 DO - http://doi.org/10.4208/jcm.1203-m3977 UR - https://global-sci.org/intro/article_detail/jcm/8450.html KW - Finite element method, Eigenvalue recovery, Ultraconvergence AB -

The classical eigenvalue problem of the second-order elliptic operator is approximated with bi-quadratic finite element in this paper. We construct a new superconvergent function recovery operator, from which the $O(h^8|\ln h|^2)$ ultraconvergence of eigenvalue approximation is obtained. Numerical experiments verify the theoretical results.

Lingxiong Meng and Zhimin Zhang. (2012). The Ultraconvergence of Eigenvalues for Bi-Quadratic Finite Elements. Journal of Computational Mathematics. 30 (5). 555-564. doi:10.4208/jcm.1203-m3977
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