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Journal Articles Computational Methods in Applied Mathematics Year : 2019

A New Probabilistic Interpretation of the Bramble–Hilbert Lemma

Joël Chaskalovic
Franck Assous

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 the 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.
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Dates and versions

hal-03837965 , version 1 (03-11-2022)

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Joël Chaskalovic, Franck Assous. A New Probabilistic Interpretation of the Bramble–Hilbert Lemma. Computational Methods in Applied Mathematics, 2019, 20, pp.79 - 87. ⟨10.1515/cmam-2018-0270⟩. ⟨hal-03837965⟩
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