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Probabilistic Approach to Characterize Quantitative Uncertainty in Numerical Approximations

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”.

Keyword : probabilistic models, data mining, quantitative uncertainty, finite elements, Big Data

How to Cite
Chaskalovic, J., & Assous, F. (2017). Probabilistic Approach to Characterize Quantitative Uncertainty in Numerical Approximations. Mathematical Modelling and Analysis, 22(1), 106-120. https://doi.org/10.3846/13926292.2017.1272499
Published in Issue
Jan 11, 2017
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This work is licensed under a Creative Commons Attribution 4.0 International License.