TY - JOUR
T1 - A Discussion on Two Stochastic Elliptic Modeling Strategies
AU - Xiaoliang Wan
JO - Communications in Computational Physics
VL - 3
SP - 775
EP - 796
PY - 2012
DA - 2012/11
SN - 11
DO - http://doi.org/10.4208/cicp.300610.140411a
UR - https://global-sci.org/intro/article_detail/cicp/7391.html
KW - 
AB - <p style="text-align: justify;">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<sup>−1</sup>)<sup>⋄</sup><sup>(−1)</sup>⋄∇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 l<sub>c</sub>. Numerical results are presented for both one- and two-dimensional cases</p>