  The aim of this paper is to provide new perspectives on the relative finite
elements accuracy. Starting from a geometrical interpretation of the error
estimate which can be deduced from Bramble-Hilbert lemma, we derive a
probability law that evaluates the relative accuracy, considered as a random
variable, between two finite elements $P_k$ and $P_m$, ($k < m$). We extend
this probability law to get a cumulated probabilistic law for two main
applications. The first one concerns a family of meshes and the second one is
dedicated to a sequence of simplexes which constitute a given mesh. Both of
this applications might be relevant for adaptive mesh refinement.
