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Correction of finite element eigenvalues for problems with natural or periodic boundary conditions. (English) Zbl 0646.65070
Let ${\lambda }_{1},{\lambda }_{2},··$. denote the eigenvalues of the Sturm- Liouville problem $-{y}^{\text{'}\text{'}}+qy=\lambda y$, ${\delta }_{1}{y}^{\text{'}}\left(0\right)+{\sigma }_{2}y\left(0\right)={\sigma }_{3}{y}^{\text{'}}\left(\pi \right)+{\sigma }_{4}y\left(\pi \right)=0·$ For the case of natural and periodic boundary conditions and a finite element approximation on a uniform mesh of width $h=\pi /n$ an asymptotic correction technique, developed by J. W. Paine, F. R. de Hoog and R. S. Anderssen [Computing 26, 123-139 (1981; Zbl 0436.65063)] reduces the error of the approximation of ${\lambda }_{k}$ from $O\left({k}^{4}{h}^{2}\right)$ to $O\left(k{h}^{2}\right)$. As numerical results show, the new technique is useful already for low values of k.
Reviewer: L.Elsner

##### MSC:
 65L15 Eigenvalue problems for ODE (numerical methods) 65L60 Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE 34L99 Ordinary differential operators
##### References:
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