@inproceedings{b448217c6c344b279d67ff63a2077185,
title = "An Improved Interpolation Error Estimate from a New Taylor-Like Formula: Application to Finite Element Method",
abstract = "In this paper, we propose an improved interpolation error estimate based on a new Taylor-like formula, which we apply to the finite element method. We first present a new first-order and second-order expansion formula with a reduced remainder. Then, we derive a new interpolation error estimate in W1,p. We compare this with the classical error estimates based on the standard Taylor formula and the corresponding interpolation error estimate derived from the mean value theorem. We illustrate, with examples, the significant reduction this yields in finite element computation costs.",
keywords = "Approximation error, Finite elements, Interpolation error, Taylor-like formula, Taylor{\textquoteright}s theorem",
author = "Jo{\"e}l Chaskalovic and Franck Assous",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.; 11th International Conference on New Trends in the Applications of Differential Equations in Sciences, NTADES 2024 ; Conference date: 07-07-2024 Through 10-07-2024",
year = "2025",
doi = "10.1007/978-3-031-83398-4\_22",
language = "אנגלית",
isbn = "9783031833977",
series = "Springer Proceedings in Mathematics and Statistics",
pages = "277--290",
editor = "Angela Slavova",
booktitle = "New Trends in the Applications of Differential Equations in Sciences - NTADES 2024",
}