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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