https://hal-cnrs.archives-ouvertes.fr/hal-03832215Chaskalovic, JoëlJoëlChaskalovicSU - Sorbonne UniversitéAssous, FranckFranckAssousOn Generalized Binomial Laws to Evaluate Finite Element Accuracy: Preliminary Probabilistic Results for Adaptive Mesh RefinementHAL CCSD2020Error estimatesProbabilityFinite elements FEBramble-Hilbert LemmaMesh refinement[MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA][MATH.MATH-PR] Mathematics [math]/Probability [math.PR]Chaskalovic, Joël2022-10-27 14:54:432022-11-04 03:54:312022-11-02 09:17:03enJournal articleshttps://hal-cnrs.archives-ouvertes.fr/hal-03832215/document10.1515/jnma-2019-0001application/pdf1The 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 Pk and Pm , 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, the second one is dedicated to a sequence of simplexes constituting a given mesh. Both of these applications could be considered as a first step toward application for adaptive mesh refinement with probabilistic methods.