Correction of finite element estimates for Sturm-Liouville eigenvalues |
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Authors: | Alan L. Andrew John W. Paine |
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Affiliation: | (1) Mathematics Department, La Trobe University, 3083 Bundoora, Victoria, Australia;(2) Department of Geology and Geophysics, University of Adelaide, 5001 Adelaide, S.A., Australia |
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Abstract: | Summary It is shown that a simple asymptotic correction technique of Paine, de Hoog and Anderssen reduces the error in the estimate of thekth eigenvalue of a regular Sturm-Liouville problem obtained by the finite element method, with linear hat functions and mesh lengthh, fromO(k4h2) toO(k h2). The result still holds when the matrix elements are evaluated by Simpson's rule, but if the trapezoidal rule is used the error isO(k2h2). Numerical results demonstrate the usefulness of the correction even for low values ofk. |
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Keywords: | AMS(MOS): 65L15 CR: G1.7 |
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