@inproceedings{61f0497030c34d4e89301f2731fb5ef9,
title = "From a Geometrical Interpretation of Bramble-Hilbert Lemma to a Probability Distribution for Finite Element Accuracy",
abstract = "The aim of this paper is to provide new perspectives on relative finite element accuracy which is usually based on the asymptotic speed of convergence comparison when the mesh size h goes to zero. Starting from a geometrical reading of the error estimate due to Bramble-Hilbert lemma, we derive two probability distributions that estimate the relative accuracy, considered as a random variable, between two Lagrange finite elements P:k and P:m, (k < m ). We establish mathematical properties of these probabilistic distributions and we get new insights which, among others, show that P:k or P:m is more likely accurate than the other, depending on the value of the mesh size h.",
keywords = "Bramble-Hilbert lemma, Error estimates, Finite elements, Probability",
author = "Joel Chaskalovic and Franck Assous",
note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG.; 7th International Conference on Finite Difference Methods, FDM 2018 ; Conference date: 11-06-2018 Through 16-06-2018",
year = "2019",
doi = "https://doi.org/10.1007/978-3-030-11539-5_1",
language = "الإنجليزيّة",
isbn = "9783030115388",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "3--14",
editor = "Ivan Dimov and Istv{\'a}n Farag{\'o} and Lubin Vulkov",
booktitle = "Finite Difference Methods. Theory and Applications - 7th International Conference, FDM 2018, Revised Selected Papers",
address = "ألمانيا",
}