A refined first-order expansion formula in Rn: Application to interpolation and finite element error estimates
Numerical Analysis
2022-10-03 v1 Numerical Analysis
Abstract
The aim of this paper is to derive a refined first-order expansion formula in Rn, the goal being to get an optimal reduced remainder, compared to the one obtained by usual Taylor's formula. For a given function, the formula we derived is obtained by introducing a linear combination of the first derivatives, computed at equally spaced points. We show how this formula can be applied to two important applications: the interpolation error and the finite elements error estimates. In both cases, we illustrate under which conditions a significant improvement of the errors can be obtained, namely how the use of the refined expansion can reduce the upper bound of error estimates.
Keywords
Cite
@article{arxiv.2209.15286,
title = {A refined first-order expansion formula in Rn: Application to interpolation and finite element error estimates},
author = {Joel Chaskalovic and Franck Assous},
journal= {arXiv preprint arXiv:2209.15286},
year = {2022}
}
Comments
20 pages