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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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
Keywords
- Eigenvalue problem
- biharmonic equation
- Ciarlet–Raviart scheme
- asymptotic expansion
- extrapolation
- a posteriori error estimate