Error estimate evaluation in numerical approximations of partial differential equations: A pilot study using data mining methods

Franck Assous, Joël Chaskalovic

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

In this Note, we propose a new methodology based on exploratory data mining techniques to evaluate the errors due to the description of a given real system. First, we decompose this description error into four types of sources. Then, we construct databases of the entire information produced by different numerical approximation methods, to assess and compare the significant differences between these methods, using techniques like decision trees, Kohonen's cards, or neural networks. As an example, we characterize specific states of the real system for which we can locally appreciate the accuracy between two kinds of finite elements methods. In this case, this allowed us to precise the classical Bramble-Hilbert theorem that gives a global error estimate, whereas our approach gives a local error estimate.

Original languageEnglish
Pages (from-to)304-313
Number of pages10
JournalComptes Rendus - Mecanique
Volume341
Issue number3
DOIs
StatePublished - Mar 2013
Externally publishedYes

Keywords

  • Asymptotic analysis
  • Data mining
  • Error estimate
  • Paraxial model
  • Vlasov-Maxwell equations

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