Numerical Analysis and Applications

, Volume 10, Issue 3, pp 259–271 | Cite as

Solution of a stochastic Darcy equation by polynomial chaos expansion

  • I. A. ShalimovaEmail author
  • K. K. Sabelfeld


This paper deals with solving a boundary value problem for the Darcy equation with a random hydraulic conductivity field.We use an approach based on polynomial chaos expansion in a probability space of input data.We use a probabilistic collocation method to calculate the coefficients of the polynomial chaos expansion. The computational complexity of this algorithm is determined by the order of the polynomial chaos expansion and the number of terms in the Karhunen–Loève expansion. We calculate various Eulerian and Lagrangian statistical characteristics of the flow by the conventional Monte Carlo and probabilistic collocation methods. Our calculations show a significant advantage of the probabilistic collocation method over the directMonte Carlo algorithm.


polynomial chaos probabilistic collocation method Darcy equation Monte Carlo method Karhunen–Loève expansion 


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© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Institute of Computational Mathematics and Mathematical Geophysics, Siberian BranchRussian Academy of SciencesNovosibirskRussia

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