Probabilitic Approach to Characterize Quantitative Uncertainty in Numerical Approximations - Archive ouverte HAL Access content directly
Journal Articles Mathematical Modelling and Analysis Year : 2017

Probabilitic Approach to Characterize Quantitative Uncertainty in Numerical Approximations

(1) ,
1
Joel Chaskalovic
  • Function : Author
  • PersonId : 1181612
Franck Assous

Abstract

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".
Fichier principal
Vignette du fichier
Math_Model_2017.pdf (1.16 Mo) Télécharger le fichier
Origin : Publisher files allowed on an open archive

Dates and versions

hal-03838096 , version 1 (03-11-2022)

Identifiers

Cite

Joel Chaskalovic, Franck Assous. Probabilitic Approach to Characterize Quantitative Uncertainty in Numerical Approximations. Mathematical Modelling and Analysis, 2017, 22, pp.106 - 120. ⟨10.3846/13926292.2017.1272499⟩. ⟨hal-03838096⟩
0 View
0 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More