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 the Bramble-Hilbert lemma, we derive two probability distributions that estimate the relative accuracy, considered as a random variable, between two Lagrange finite elements Pk and Pm (k < m). We establish mathematical properties of these probabilistic distributions and we get new insights which, among others, show that Pk or Pm is more likely accurate than the other, depending on the value of the mesh size h.
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- Bramble-Hilbert Lemma
- Error Estimates
- Finite Elements