A Discussion on Two Stochastic Elliptic Modeling Strategies

Authors

  • Xiaoliang Wan

DOI:

https://doi.org/10.4208/cicp.300610.140411a

Abstract

Based on the study of two commonly used stochastic elliptic models: I:−∇· (a(x,ω)·∇u(x,ω))=f(x) and II:−∇·(a(x,ω)⋄∇u(x,ω))=f(x), we constructed a new stochastic elliptic model III: −∇· (a−1)(−1)⋄∇u(x,ω))=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 lc. Numerical results are presented for both one- and two-dimensional cases

Published

2012-11-01

Issue

Section

Articles