English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The aim of this paper is to derive a refined first-order expansion formula inRn, the goal being to get an optimal reduced remainder, compared to the oneobtained by usual Taylor's formula. For a given function, the formula wederived is obtained by introducing a linear combination of the firstderivatives, computed at $n+1$ equally spaced points. We show how this formulacan be applied to two important applications: the interpolation error and thefinite elements error estimates. In both cases, we illustrate under whichconditions a significant improvement of the errors can be obtained, namely howthe use of the refined expansion can reduce the upper bound of error estimates.

A refined first-order expansion formula in Rn: Application to interpolation and finite element error estimates