Anisotropic interpolation error estimates using a new geometric parameter
Numerical Analysis
2022-08-03 v3 Numerical Analysis
Abstract
We present precise anisotropic interpolation error estimates for smooth functions using a new geometric parameter and derive inverse inequalities on anisotropic meshes. In our theory, the interpolation error is bounded in terms of the diameter of a simplex and the geometric parameter. Imposing additional assumptions makes it possible to obtain anisotropic error estimates. This paper also includes corrections to an error in Theorem 2 of our previous paper, "General theory of interpolation error estimates on anisotropic meshes" (Japan Journal of Industrial and Applied Mathematics, 38 (2021) 163-191).
Cite
@article{arxiv.2106.03339,
title = {Anisotropic interpolation error estimates using a new geometric parameter},
author = {Hiroki Ishizaka and Kenta Kobayashi and Takuya Tsuchiya},
journal= {arXiv preprint arXiv:2106.03339},
year = {2022}
}
Comments
36 pages, 12 figures