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

09/30/2022
by   Joël Chaskalovic, et al.
0

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 n+1 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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/17/2023

A new second order Taylor-like theorem with an optimized reduced remainder

In this paper, we derive a variant of the Taylor theorem to obtain a new...
research
07/06/2020

Refined Analysis of the Asymptotic Complexity of the Number Field Sieve

The classical heuristic complexity of the Number Field Sieve (NFS) is th...
research
12/28/2021

A New First Order Taylor-like Theorem With An Optimized Reduced Remainder

This paper is devoted to a new first order Taylor-like formula where the...
research
02/12/2023

Pointwise error estimates and local superconvergence of Jacobi expansions

As one myth of polynomial interpolation and quadrature, Trefethen [30] r...
research
11/26/2019

Brezzi-Douglas-Marini interpolation of any order on anisotropic triangles and tetrahedra

Recently, the H⃗(div)-conforming finite element families for second orde...
research
02/23/2021

Transfer function interpolation remainder formula of rational Krylov subspace methods

Rational Krylov subspace projection methods are one of successful method...
research
02/06/2023

A simple formula of the magnetic potential and of the stray field energy induced by a given magnetization

The primary aim of this paper is the derivation and the proof of a simpl...

Please sign up or login with your details

Forgot password? Click here to reset