Korean J. Math. Vol. 28 No. 3 (2020) pp.587-601
DOI: https://doi.org/10.11568/kjm.2020.28.3.587

Enhancing eigenvalue approximation with Bank--Weiser error estimators

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Published: Sep 30, 2020
Keywords:
eigenvalue problem, finite element method, error estimator, superconvergence
Mathematics Subject Classification:
65N15, 65N25, 65N30

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Kwang-Yeon Kim
Department of Mathematics, Kangwon National University Chuncheon 24341, Korea

Abstract

In this paper we propose a way of enhancing eigenvalue approximations with the Bank--Weiser error estimators for the P1 and P2 conforming finite element methods of the Laplace eigenvalue problem. It is shown that we can achieve two extra orders of convergence than those of the original eigenvalue approximations when the corresponding eigenfunctions are smooth and the underlying triangulations are strongly regular. Some numerical results are presented to demonstrate the accuracy of the enhanced eigenvalue approximations.



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References

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