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 \(P_m\), (\(k < m\)). We establish mathematical properties of these probabilistic distributions and we get new insights which, among others, show that \(P_k\) or \(P_m\) is more likely accurate than the other, depending on the value of the mesh size h.
Error estimates Finite elements Bramble-Hilbert lemma Probability
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