Asymptotic expansion and extrapolation for the Eigenvalue approximation of the biharmonic eigenvalue problem by Ciarlet–Raviart scheme |
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| Authors: | Wei Chen Qun Lin |
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| Institution: | (1) School of Economics, Shandong University, Jinan, 250100, People’s Republic of China;(2) Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Academia Sinica, Beijing, 100080, People’s Republic of China |
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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.
This author was supported by China Postdoctoral Sciences Foundation. |
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| Keywords: | Eigenvalue problem biharmonic equation Ciarlet– Raviart scheme asymptotic expansion extrapolation a posteriori error estimate |
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