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arXiv · 1803.09552

A new mixed functional-probabilistic approach for finite element accuracy

Joël Chaskalovic·Franck Assous
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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 qualified the relative accuracy in the case of high order finite elements are correspondingly obtained.

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Joël Chaskalovic, Franck Assous. 2018-03-26. A new mixed functional-probabilistic approach for finite element accuracy. https://arxiv.org/abs/1803.09552

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