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Crouzeix–Raviart and Raviart–Thomas finite-element error analysis on anisotropic meshes violating the maximum-angle condition

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Abstract

We investigate the piecewise linear nonconforming Crouzeix–Raviart and the lowest order Raviart–Thomas finite-element methods for the Poisson problem on three-dimensional anisotropic meshes. We first give error estimates of the Crouzeix–Raviart and the Raviart–Thomas finite-element approximate problems. We next present the equivalence between the Raviart–Thomas finite-element method and the enriched Crouzeix–Raviart finite-element method. We emphasize that we do not impose either shape-regular or maximum-angle condition during mesh partitioning. Numerical results confirm the results that we obtained.

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Notes

  1. Note added in proof. [16,Theorem 2] is incorrect. See the erratum in https://arxiv.org/abs/2002.09721

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Acknowledgements

This work was supported by JSPS KAKENHI Grant Number JP16H03950. We would like to thank the anonymous referee for the valuable comments.

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Authors and Affiliations

  1. Graduate School of Science and Engineering, Ehime University, Matsuyama, Japan

    Hiroki Ishizaka & Takuya Tsuchiya

  2. Graduate School of Business Administration, Hitotsubashi University, Kunitachi, Japan

    Kenta Kobayashi

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  1. Hiroki Ishizaka
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  2. Kenta Kobayashi
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  3. Takuya Tsuchiya
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Correspondence to Hiroki Ishizaka.

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Ishizaka, H., Kobayashi, K. & Tsuchiya, T. Crouzeix–Raviart and Raviart–Thomas finite-element error analysis on anisotropic meshes violating the maximum-angle condition . Japan J. Indust. Appl. Math. 38, 645–675 (2021). https://doi.org/10.1007/s13160-020-00455-7

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  • DOI: https://doi.org/10.1007/s13160-020-00455-7

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