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On Generalized Binomial Laws to Evaluate Finite Element Accuracy: Preliminary Probabilistic Results for Adaptive Mesh Refinement

Abstract : The aim of this paper is to provide new perspectives on the relative finite elements accuracy. Starting from a geometrical interpretation of the error estimate which can be deduced from Bramble-Hilbert lemma, we derive a probability law that evaluates the relative accuracy, considered as a random variable, between two finite elements Pk and Pm , k < m. We extend this probability law to get a cumulated probabilistic law for two main applications. The first one concerns a family of meshes, the second one is dedicated to a sequence of simplexes constituting a given mesh. Both of these applications could be considered as a first step toward application for adaptive mesh refinement with probabilistic methods.
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https://hal-cnrs.archives-ouvertes.fr/hal-03832215
Contributor : joel chaska Connect in order to contact the contributor
Submitted on : Thursday, October 27, 2022 - 2:54:43 PM
Last modification on : Friday, November 4, 2022 - 3:54:31 AM

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Joël Chaskalovic, Franck Assous. On Generalized Binomial Laws to Evaluate Finite Element Accuracy: Preliminary Probabilistic Results for Adaptive Mesh Refinement. Journal of Numerical Mathematics, 2020, 28, pp.63 - 74. ⟨10.1515/jnma-2019-0001⟩. ⟨hal-03832215⟩

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