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A New Probabilistic Interpretation of the Bramble–Hilbert Lemma

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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https://hal-cnrs.archives-ouvertes.fr/hal-03837965
Contributor : joel chaska Connect in order to contact the contributor
Submitted on : Thursday, November 3, 2022 - 11:34:53 AM
Last modification on : Tuesday, November 8, 2022 - 4:00:30 AM

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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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