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Volume 11, Issue 3
A Discussion on Two Stochastic Elliptic Modeling Strategies

Xiaoliang Wan

DOI: 10.4208/cicp.300610.140411a

Commun. Comput. Phys., 11 (2012), pp. 775-796.

Published online: 2012-11

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  • 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

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@Article{CiCP-11-775, author = {Xiaoliang Wan}, title = {A Discussion on Two Stochastic Elliptic Modeling Strategies}, journal = {Communications in Computational Physics}, year = {2012}, volume = {11}, number = {3}, pages = {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

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.300610.140411a}, url = {http://global-sci.org/intro/article_detail/cicp/7391.html} }
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 -

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

Xiaoliang Wan. (2012). A Discussion on Two Stochastic Elliptic Modeling Strategies. Communications in Computational Physics. 11 (3). 775-796. doi:10.4208/cicp.300610.140411a
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