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A Discussion on Two Stochastic Elliptic Modeling Strategies

Published online by Cambridge University Press:  20 August 2015

Xiaoliang Wan
Xiaoliang Wan*
Affiliation:
Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803, USA
*
*Corresponding author.Email:[email protected]
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Abstract

Based on the study of two commonly used stochastic elliptic models: I: − ∇· (a(x,w)·∇u(x,w)) = f (x) and II: − ∇·(a(x,w)◊∇u(x,w)) = f (x), we constructed a new stochastic elliptic model III: −∇ ◊ ((a−1)·(−1)◊∇u(x,w)) = f (x), in. The difference between models I and II is twofold: a scaling factor induced by the way of applying the Wick product and the regularization induced by the Wick product itself. In, we showed that model III has the same scaling factor as model I. In this paper we present a detailed discussion about the difference between models I and III with respect to the two characteristic parameters of the random coefficient, i.e., the standard deviation σ and the correlation length lc. Numerical results are presented for both one- and two-dimensional cases.

Keywords

60H1565C2065C30Wiener chaosstochastic PDEstochastic modelingstochastic finite element method
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 3 , March 2012 , pp. 775 - 796
Copyright
Copyright © Global Science Press Limited 2012

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