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Computable Interpolation Error Constants for the Geometric Simplex Finite Elements

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Abstract

In this paper, a novel high accuracy computation method for interpolation error constants is proposed over the geometric simplex finite elements. Firstly, the expansions of bounded linear operators are employed to derive the explicit estimate of interpolation error constants, which depend only on the shape of the geometric simplex finite elements and the definition of interpolation functions. Then, this method is applied to the linear interpolation function, and the results are consistent with our analysis. Finally, some numerical examples are given to validate our analysis. Such high accuracy computation method for interpolation error constants are beneficial attempts to accelerate the adaptive computation and verification of finite element solutions.

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Acknowledgements

The authors gratefully appreciate the valuable comments from the reviewers, which have contributed significantly to the improvement of this manuscript. This research was supported by the Science Challenge Project (No. TZ2018001), National Natural Science Foundation of China (Nos. 11871467, 11371331, 11301392), Shanghai Peak Discipline Program for Higher Education Institutions (Class I)-Civil Engineering, and Fundamental Research Funds for the Central Universities (No. 22120180529).

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Authors and Affiliations

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

    Tingting Hao & Xiaofei Guan

  2. LSEC and Institute of Computational Mathematics, Academy of Mathematics and Systems Science, University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing, 100190, PR, China

    Shipeng Mao

  3. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, China

    Shaochun Chen

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  1. Tingting Hao
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  2. Xiaofei Guan
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  4. Shaochun Chen
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Correspondence to Xiaofei Guan.

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Hao, T., Guan, X., Mao, S. et al. Computable Interpolation Error Constants for the Geometric Simplex Finite Elements. J Sci Comput 87, 35 (2021). https://doi.org/10.1007/s10915-021-01449-4

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