Abstract
We propose a general theory of estimating interpolation error for smooth functions in two and three dimensions. In our theory, the error of interpolation is bound in terms of the diameter of a simplex and a geometric parameter. In the two-dimensional case, our geometric parameter is equivalent to the circumradius of a triangle. In the three-dimensional case, our geometric parameter also represents the flatness of a tetrahedron. Through the introduction of the geometric parameter, the error estimates newly obtained can be applied to cases that violate the maximum-angle condition.
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27 March 2023
A Correction to this paper has been published: https://doi.org/10.1007/s13160-023-00582-x
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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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Ishizaka, H., Kobayashi, K. & Tsuchiya, T. General theory of interpolation error estimates on anisotropic meshes. Japan J. Indust. Appl. Math. 38, 163–191 (2021). https://doi.org/10.1007/s13160-020-00433-z
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DOI: https://doi.org/10.1007/s13160-020-00433-z