Year: 2012
Communications in Computational Physics, Vol. 11 (2012), Iss. 3 : pp. 775–796
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
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.300610.140411a
Communications in Computational Physics, Vol. 11 (2012), Iss. 3 : pp. 775–796
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
-
The Wick--Malliavin Approximation of Elliptic Problems with Log-Normal Random Coefficients
Wan, Xiaoliang | Rozovskii, Boris L.SIAM Journal on Scientific Computing, Vol. 35 (2013), Iss. 5 P.A2370
https://doi.org/10.1137/130918605 [Citations: 7] -
Numerical Methods for Stochastic Partial Differential Equations with White Noise
Multiplicative white noise: The Wick-Malliavin approximation
Zhang, Zhongqiang | Karniadakis, George Em2017
https://doi.org/10.1007/978-3-319-57511-7_11 [Citations: 0]