General theory of interpolation error estimates on anisotropic meshes
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説明
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.
29 pages, 2 figures. In "General theory of interpolation error estimates on anisotropic meshes" (Japan Journal of Industrial and Applied Mathematics, 38 (2021) 163-191), Theorem 2 has been found to be incorrect and misleading. Corrections to an error are given in "General theory of interpolation error estimates on anisotropic meshes, part II", arXiv:2106.03339
収録刊行物
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- Japan Journal of Industrial and Applied Mathematics
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Japan Journal of Industrial and Applied Mathematics 38 (1), 163-191, 2020-07-27
Springer Science and Business Media LLC
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詳細情報 詳細情報について
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- CRID
- 1362823123420355328
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- NII論文ID
- 210000175823
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- ISSN
- 1868937X
- 09167005
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- 資料種別
- journal article
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- データソース種別
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- CiNii Articles
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