Asymptotic expansion and extrapolation for the eigenvalue approximation of the biharmonic eigenvalue problem by Ciarlet-Raviart scheme. (English) Zbl 1122.65106

The paper deals with a new Ciarlet-Raviart mixed scheme for solving the biharmonic eigenvalue problem with bilinear finite elements. This method provides higher order convergence rate for eigenvalues and eigenfunctions approximations. Furthermore, an asymptotic expansion of the eigenvalue error is given which is then used to derive an efficient extrapolation and a posteriori error estimate for eigenvalues. The results are illustrated by some numerical experiments.


65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
35P15 Estimates of eigenvalues in context of PDEs
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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