(untitled) (Communications in Computational Physics, 2012)
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