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Zbl 1151.65086
Jia, Shanghui; Xie, Hehu; Yin, Xiaobo; Gao, Shaoqin
Approximation and eigenvalue extrapolation of biharmonic eigenvalue problem by nonconforming finite element methods. (English)
[J] Numer. Methods Partial Differ. Equations 24, No. 2, 435-448 (2008). ISSN 0749-159X; ISSN 1098-2426/e

This paper deals with the eigenvalue problem $\Delta^2 u=\lambda\rho u$ in $\Omega$, $u= {\partial u\over\partial n}= 0$ on $\partial\Omega$, $\int_\Omega\rho u^2= 1$. The authors analyze this problem by two nonconforming finite element methods and obtain a full order convergence rate of the eigenvalue approximations.
[Pavol Chocholatý (Bratislava)]

MSC 2000:: *65N25 Numerical methods for eigenvalue problems (BVP of PDE)
65N30 Finite numerical methods (BVP of PDE)
65N12 Stability and convergence of numerical methods (BVP of PDE)
35P15 Estimation of eigenvalues for PD operators

Keywords: asymptotic expansions; biharmonic eigenvalue problem; extrapolation; nonconforming finite element methods; convergence

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