A Discussion on Two Stochastic Elliptic Modeling Strategies

Abstract

AbstractBased 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. 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, 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.