We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itˆo chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. To obtain the chaos coefficients in the corresponding deterministic equations, we use a least square formulation. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.<\/p>\r\n","references":"[1] F. E. Benth and J. Gjerde, Convergence rates for finite element approximations of stochastic partial differential equations, Stochastics Stochastics Rep. 63 (1998) 313\u2013326.\r\n[2] R. Glowinski, Numerical methods for nonlinear variational problems. Springer, 2008.\r\n[3] H. Holden, T. Lindstr\u00f8m, B. \u00d8ksendal, J. Ub\u00f8e, and T.-S. Zhang, The pressure equation for fluid flow in a stochastic medium, Potential Analysis, 4 (1995) 655\u2013674.\r\n[4] H. Holden, B. \u00d8ksendal, J. Ub\u00f8e, and T.-S. Zhang, Stochastic Partial Differential Equations. A Modeling, White Noise Functional Approach, Probability and its Applications. Birkh\u00a8auser, Boston, 1996.\r\n[5] M. Kardar, Y.C. Zhang, Scaling of Directed Polymers in Random Media, Physical Review Letters, 58 (1987) 2087\u20132090.\r\n[6] H. Manouzi, A finite element approximation of linear stochastic PDE\u2019s equations driven by a multiplicative white noise, International Journal of Computer Mathematics, 85 (2008) 527\u2013546.\r\n[7] T. G. Theting, Solving Wick-stochastic boundary value problems using a finite element method, Stochastics Stochastics Rep. 70 (200) 241\u2013270.\r\n[8] T.G. Theting, Solving Parabolic Wick-Stochastic Boundary Value Problems Using a Finite Element Method, Stochast. Stochast. Reports. 75 (2003) 57\u201392.\r\n[9] G. V\u02daage, Hilbert space methods applied to elliptic stochastic partial differential equations, Stochastic analysis and related topics, Stochastic analysis and related topics, Progr. Probab. 38, Birkh\u00a8auser Boston, Boston, MA, 1996, pp. 281\u2013294.\r\n[10] G.V\u02daage, Variational Methods for PDEs Applied to Stochastic Partial Differential Equations, Math. Scand. 82 (1998) 113\u2013137.\r\n[11] Wuan Luo, Wiener chaos expansion and numerical solutions of stochastic partial differential equations. VDM Verlay Edition, 2010.\r\n[12] T. Zhang, Characterization of white noise test functions and Hida distributions, Stochastics 41, pp 71\u201378, 1980.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 85, 2014"}