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Correction of finite element eigenvalues for problems with natural or periodic boundary conditions. (English) Zbl 0646.65070
Let λ 1 ,λ 2 ,··. denote the eigenvalues of the Sturm- Liouville problem -y '' +qy=λy, δ 1 y ' (0)+σ 2 y(0)=σ 3 y ' (π)+σ 4 y(π)=0· For the case of natural and periodic boundary conditions and a finite element approximation on a uniform mesh of width h=π/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 λ k from O(k 4 h 2 ) to O(kh 2 ). As numerical results show, the new technique is useful already for low values of k.
Reviewer: L.Elsner

65L15Eigenvalue problems for ODE (numerical methods)
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
34L99Ordinary differential operators
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