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Journal Articles Lecture Notes in Computer Science Year : 2019

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 Pm, (k < m). We establish mathematical properties of these probabilistic distributions and we get new insights which, among others, show that P k or Pm is more likely accurate than the other, depending on the value of the mesh size h.
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Dates and versions

hal-03837971 , version 1 (10-11-2022)

Licence

Attribution - CC BY 4.0

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Joël Chaskalovic, Franck Assous. From a Geometrical Interpretation of Bramble-Hilbert Lemma to a Probability Distribution for Finite Element Accuracy. Lecture Notes in Computer Science, 2019, Lecture Notes in Computer Science, pp.3-14. ⟨10.1007/978-3-030-11539-5_1⟩. ⟨hal-03837971⟩
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