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The Lower/Upper Bound Property of the Crouzeix–Raviart Element Eigenvalues on Adaptive Meshes

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Abstract

In this paper we first discover and prove that on adaptive meshes the eigenvalues by the Crouzeix–Raviart element approximate the exact ones from below when the corresponding eigenfunctions are singular. In addition, we use conforming finite elements to do the interpolation postprocessing to get the upper bound of the eigenvalues. Using the upper and lower bounds of eigenvalues we design the control condition of adaptive algorithm, and some numerical experiments are carried out under the package of Chen to validate our theoretical results.

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Acknowledgments

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

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Guizhou Normal University, Guiyang, 550001, China

    Yidu Yang, Jiayu Han, Hai Bi & Yuanyuan Yu

Authors
  1. Yidu Yang
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  2. Jiayu Han
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  3. Hai Bi
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  4. Yuanyuan Yu
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Correspondence to Yidu Yang.

Additional information

Project supported by the National Natural Science Foundation of China (Grant Nos. 11161012 , 11201093).

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Yang, Y., Han, J., Bi, H. et al. The Lower/Upper Bound Property of the Crouzeix–Raviart Element Eigenvalues on Adaptive Meshes. J Sci Comput 62, 284–299 (2015). https://doi.org/10.1007/s10915-014-9855-8

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  • DOI: https://doi.org/10.1007/s10915-014-9855-8

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