### THE ULTRACONVERGENCE OF EIGENVALUES FORBI-QUADRATIC FINITE ELEMENTS

Lingxiong Meng, Zhimin Zhang

1. 1. Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP)(Ministry of Education of China), College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, China;
2. Department of Mathematics, Wayne State University, Detroit, MI 48202, USA and Guangdong Province Key Laboratory of Computational Science, School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, China
• Received:2011-12-14 Revised:2012-03-06 Online:2012-09-15 Published:2012-09-24
• Supported by:

The work of the rst author was supported by the National NaturalScience Foundation of China (10671078) and the China Scholarship Council (CSC) as a visitingscholar in Wayne State University. The research of the second author was supported in part bythe US National Science Foundation through grant DMS-1115530, the Ministry of Education of China through the Changjiang Scholars program, the Guangdong Provincial Government of China through the \Computational Science Innovative Research Team program, and Guang-dong Province Key Laboratory of Computational Science at the Sun Yat-sen University.

Lingxiong Meng, Zhimin Zhang. THE ULTRACONVERGENCE OF EIGENVALUES FORBI-QUADRATIC FINITE ELEMENTS[J]. Journal of Computational Mathematics, 2012, 30(5): 555-564.

The classical eigenvalue problem of the second-order elliptic operator is approximatedwith bi-quadratic nite element in this paper. We construct a new superconvergent functionrecovery operator, from which the O(h8|lnh|2) ultraconvergence of eigenvalue approxima-tion is obtained. Numerical experiments verify the theoretical results.

CLC Number:

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