  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.

Numerical Analysis