Error Analysis of Lagrange Interpolation on Tetrahedrons

Kenta Kobayashi, Takuya Tsuchiya

Published 2016-06-13Version 1

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. It should be emphasized that we do not impose any geometric restrictions on the tetrahedron itself.