Probabilistic Approach to Characterize Quantitative Uncertainty in Numerical Approximations. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Chaskalovic, Joel; Assous, Franck
• Is Part Of: Mathematical modelling and analysis. Volume 22:Issue 1(2017)
• Page Start: 106
• Page End: 120
• Publication Date: 2017-01-02
• Subjects: probabilistic models -- data mining -- quantitative uncertainty -- finite elements -- Big Data; 65P25 -- 77C10; Mathematical models -- Periodicals; Mathematical models -- Study and teaching -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis -- Problems, exercises, etc -- Periodicals; Mathematical analysis; Mathematical models; Mathematical models -- Study and teaching; Periodicals; Problems and exercises; 511.805
• DOI: 10.3846/13926292.2017.1272499
• Languages: English
• ISSNs: 1392-6292

Abstract

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".