各向异性网格上插值误差估计的一般理论
数值分析
2021-06-10 v6 数值分析
摘要
我们提出一种估计二维和三维光滑函数插值误差的一般理论。在我们的理论中,插值误差由单纯形的直径和一个几何参数来界定。在二维情形,我们的几何参数等价于三角形的外接圆半径。在三维情形,我们的几何参数也表示四面体的扁平程度。通过引入该几何参数,新获得的误差估计可应用于违背最大角条件的情形。
引用
@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}
}
备注
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