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C 0IPG adaptive algorithms for the biharmonic eigenvalue problem

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Abstract

This paper focuses on C 0IPG adaptive algorithms for the biharmonic eigenvalue problem with the clamped boundary condition. We prove the reliability and efficiency of the a posteriori error indicator of the approximating eigenfunctions and analyze the reliability of the a posteriori error indicator of the approximating eigenvalues. We present two adaptive algorithms, and numerical experiments indicate that both algorithms are efficient.

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Acknowledgments

The authors cordially thank the editor and the referees for their valuable comments and suggestions that lead to the large improvement of this paper.

This work is supported by Science and Technology Foundation of Guizhou Province of China (Grant No. LH [2014] 7061) and the National Natural Science Foundation of China (Grant No.11561014).

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Authors and Affiliations

  1. School of Mathematical Sciences, Guizhou Normal University, Guiyang, 550001, China

    Hao Li & Yidu Yang

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  1. Hao Li
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  2. Yidu Yang
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Correspondence to Yidu Yang.

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Li, H., Yang, Y. C 0IPG adaptive algorithms for the biharmonic eigenvalue problem. Numer Algor 78, 553–567 (2018). https://doi.org/10.1007/s11075-017-0388-8

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  • DOI: https://doi.org/10.1007/s11075-017-0388-8

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