Numerical validation of probabilistic laws to evaluate finite element error estimates

Joël Chaskalovic, Franck Assous

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We propose a numerical validation of a probabilistic approach applied to estimate the relative accuracy between two Lagrange finite elements Pk and Pm, (k < m). In particular, we show practical cases where finite element Pk gives more accurate results than finite element Pm. This illustrates the theoretical probabilistic framework we recently derived in order to evaluate the actual accuracy. This also highlights the importance of the extra caution required when comparing two numerical methods, since the classical results of error estimates concerns only the asymptotic convergence rate.

Original languageEnglish
Pages (from-to)684-695
Number of pages12
JournalMathematical Modelling and Analysis
Issue number4
StatePublished - 28 Oct 2021
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2021 The Author(s).


  • Bramble-Hilbert lemma
  • Error estimates
  • Finite elements
  • Probability. numerical validation


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