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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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Submitted on : Thursday, November 10, 2022 - 9:54:24 AM
Last modification on : Friday, November 11, 2022 - 4:03:00 AM

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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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