A discussion on two stochastic elliptic modeling strategies

Document Type

Article

Publication Date

3-1-2012

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 [20]. 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 [20], 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 l c. Numerical results are presented for both one- and two-dimensional cases. © 2012 Global-Science Press.

Publication Source (Journal or Book title)

Communications in Computational Physics

First Page

775

Last Page

796

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