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A New Mixed Functional-Probabilistic Approach for Finite Element Accuracy

Abstract : The aim of this paper is to provide a new perspective on finite element accuracy. Starting from a geometrical reading of the Bramble-Hilbert lemma, we recall the two probabilistic laws we got in previous works that estimate the relative accuracy, considered as a random variable, between two finite elements P k and P m (k < m). Then we analyze the asymptotic relation between these two probabilistic laws when the difference m − k goes to infinity. New insights which qualify the relative accuracy in the case of high order finite elements are also obtained.
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https://hal-cnrs.archives-ouvertes.fr/hal-03832203
Contributor : joel chaska Connect in order to contact the contributor
Submitted on : Thursday, October 27, 2022 - 2:45:22 PM
Last modification on : Friday, October 28, 2022 - 3:54:02 AM

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Joël Chaskalovic, Franck Assous. A New Mixed Functional-Probabilistic Approach for Finite Element Accuracy. Computational Methods in Applied Mathematics, 2020, 20 (4), pp.799 - 813. ⟨10.1515/cmam-2019-0089⟩. ⟨hal-03832203⟩

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