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Enhancing eigenvalue approximation with Bank--Weiser error estimators

김광연
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2020.09|한국수학논문집 (Korean Journal of Mathematics)|제28권 제3호|pp. 587-601

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참고문헌

키워드

finite element methodeigenvalue problemerror estimatorsuperconvergence
주제분류수학

초록

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.

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.

참고문헌 (22)

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  13. 김광연, "Asymptotic exactness of some Bank-Weiser error estimator for quadratic triangular finite element", 대한수학회보, 57(2), pp.393~406 (2020), 대한수학회[DOI]
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