Probabilistic Approach to Characterize Quantitative Uncertainty in Numerical Approximations

Joel Chaskalovic, Franck Assous

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


This paper proposes a statistical and probabilistic approach to compare and analyze the errors of two different approximation methods. We introduce the principle of numerical uncertainty in such a process, and we illustrate it by considering the discretization difference between two different approximation orders, e.g., first and second order Lagrangian finite element. Then, we derive a probabilistic approach to define and to qualify equivalent results. We illustrate our approach on a model problem on which we built the two above mentioned finite element approximations. We consider some variables as physical “predictors”, and we characterize how they influence the odds of the approximation methods to be locally “same order accurate”.

Original languageEnglish
Pages (from-to)106-120
Number of pages15
JournalMathematical Modelling and Analysis
Issue number1
StatePublished - 2 Jan 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017 Vilnius Gediminas Technical University.


  • Big Data
  • data mining
  • finite elements
  • probabilistic models
  • quantitative uncertainty


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