Correction of finite element eigenvalues for problems with natural or periodic boundary conditions
Let \(\lambda_ 1,\lambda_ 2,..\). denote the eigenvalues of the Sturm- Liouville problem \(-y''+qy=\lambda y\), \(\delta_ 1y'(0)+\sigma_ 2y(0)=\sigma_ 3y'(\pi)+\sigma_ 4y(\pi)=0.\) 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 \textit{J. W. Paine}, \textit{F. R. de Hoog} and \textit{R. S. Anderssen} [Computing 26, 123-139 (1981; Zbl 0436.65063)] reduces the error of the approximation of \(\lambda_ k\) from \(O(k^ 4h^ 2)\) to \(O(kh^ 2)\). As numerical results show, the new technique is useful already for low values of k.
scientific article; zbMATH DE number 4054957