General theory of interpolation error estimates on anisotropic meshes
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.
Keywords
Cite
@article{arxiv.2002.09721,
title = {General theory of interpolation error estimates on anisotropic meshes},
author = {Hiroki Ishizaka and Kenta Kobayashi and Takuya Tsuchiya},
journal= {arXiv preprint arXiv:2002.09721},
year = {2021}
}
Comments
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