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A Weak Galerkin Finite Element Method Can Compute Both Upper and Lower Eigenvalue Bounds

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Abstract

In this paper, we observe an interesting phenomenon for a weak Galerkin (WG) approximation of eigenvalue problems, that is, we may obtain good approximations for exact eigenvalues from below or above, only through adjusting the global penalty parameter. Based on this observation, a high accuracy algorithm for computing eigenvalues is designed to yield higher convergence order with lower expenses. Some new techniques are developed to analyze upper and lower bound properties of eigenvalues. Numerical results supporting our theory are given.

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Acknowledgements

The authors are very grateful to the anonymous referees for their valuable suggestions and comments.

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Authors and Affiliations

  1. School of Mathematical Science, Tongji University, Shanghai, 200092, China

    Qigang Liang, Xuejun Xu & Liuyao Yuan

  2. Institute of Computational Mathematics, AMSS, Chinese Academy of Sciences, Beijing, 100190, China

    Xuejun Xu

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  1. Qigang Liang
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Correspondence to Xuejun Xu.

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The authors were supported by National Natural Science Foundation of China (Grant Nos. 12071350, 11871272), Shanghai Municipal Science and Technology Major Project No. 2021SHZDZX0100, and Science and Technology Commission of Shanghai Municipality.

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Liang, Q., Xu, X. & Yuan, L. A Weak Galerkin Finite Element Method Can Compute Both Upper and Lower Eigenvalue Bounds. J Sci Comput 93, 19 (2022). https://doi.org/10.1007/s10915-022-01986-6

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  • DOI: https://doi.org/10.1007/s10915-022-01986-6

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