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Approximation and eigenvalue extrapolation of biharmonic eigenvalue problem by nonconforming finite element methods. (English) Zbl 1151.65086

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.

MSC:

65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35P15 Estimates of eigenvalues in context of PDEs
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References:

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