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Asymptotic expansion and extrapolation for the Eigenvalue approximation of the biharmonic eigenvalue problem by Ciarlet–Raviart scheme

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Abstract

We propose and analyze the Ciarlet–Raviart mixed scheme for solving the biharmonic eigenvalue problem with bilinear finite elements. We derive a higher order convergence rate for eigenvalue and eigenfunction approximations. Furthermore, we give an asymptotic expansion of the eigenvalue error, from which an efficient extrapolation and an a posteriori error estimate for the eigenvalue are given. Finally, numerical experiments illustrating the theoretical results are reported.

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Authors and Affiliations

  1. School of Economics, Shandong University, Jinan, 250100, People’s Republic of China

    Wei Chen

  2. Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Academia Sinica, Beijing, 100080, People’s Republic of China

    Qun Lin

Authors
  1. Wei Chen
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  2. Qun Lin
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Correspondence to Wei Chen.

Additional information

Communicated by: A. Zhou.

This author was supported by China Postdoctoral Sciences Foundation.

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Chen, W., Lin, Q. Asymptotic expansion and extrapolation for the Eigenvalue approximation of the biharmonic eigenvalue problem by Ciarlet–Raviart scheme. Adv Comput Math 27, 95–106 (2007). https://doi.org/10.1007/s10444-007-9031-x

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  • DOI: https://doi.org/10.1007/s10444-007-9031-x

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