Error Analysis of Lagrange Interpolation on Tetrahedrons
Numerical Analysis
2019-09-23 v2 Numerical Analysis
Abstract
This paper describes the analysis of Lagrange interpolation errors on tetrahedrons. In many textbooks, the error analysis of Lagrange interpolation is conducted under geometric assumptions such as shape regularity or the (generalized) maximum angle condition. In this paper, we present a new estimation in which the error is bounded in terms of the diameter and projected circumradius of the tetrahedron. Because we do not impose any geometric restrictions on the tetrahedron itself, our error estimation may be applied to any tetrahedralizations of domains including very thin tetrahedrons.
Keywords
Cite
@article{arxiv.1606.03918,
title = {Error Analysis of Lagrange Interpolation on Tetrahedrons},
author = {Kenta Kobayashi and Takuya Tsuchiya},
journal= {arXiv preprint arXiv:1606.03918},
year = {2019}
}
Comments
To appear in Journal of Approximation Theory