On generalized binomial laws to evaluate finite element accuracy: Preliminary probabilistic results for adaptive mesh refinement

Joël Chaskalovic, Franck Assous

Research output: Contribution to journalArticlepeer-review

Abstract

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 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.

Original languageEnglish
Pages (from-to)63-74
Number of pages12
JournalJournal of Numerical Mathematics
Volume28
Issue number2
DOIs
StatePublished - 1 Jun 2020
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.

Keywords

  • Bramble-Hilbert lemma
  • error estimates
  • finite elements
  • mesh refinement
  • probability

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