Nonparametric probabilistic approach of uncertainties for elliptic boundary value problem

Abstract : The paper is devoted to elliptic boundary value problems With uncertainties.. Such a problem has already been analyzed in the context of the parametric probabilistic approach of system parameters uncertainties or for random media Model Uncertainties are induced by the mathematical-physical process, which allows the boundary value problem to be constructed from the design system If experiments are not available, the Bayesian approach cannot be used to take into account model uncertainties. Recently. a nonparametric probabilistic approach of both the Model Uncertainties and system parameters uncertainties has been proposed by the author to analyze Uncertain linear and non-linear dynamical systems. Nevertheless, the use of this concept that has to be developed for dynamical systems cannot directly be applied for elliptic boundary value problem. for instance, For a linear elastostatic problem relative to an elastic bounded domain We then propose an extension of the nonparametric probabilistic approach in order to take into account model uncertainties for strictly elliptic boundary Value problems. The theory and its validation are presented.
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Christian Soize. Nonparametric probabilistic approach of uncertainties for elliptic boundary value problem. International Journal for Numerical Methods in Engineering, Wiley, 2009, 80 (6-7), pp.673-688. ⟨10.1002/nme.2563⟩. ⟨hal-00684335⟩

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