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SIAMSC
2008

Mixed Multiscale Finite Element Methods for Stochastic Porous Media Flows

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Mixed Multiscale Finite Element Methods for Stochastic Porous Media Flows
In this paper, we propose a stochastic mixed multiscale finite element method. The proposed method solves the stochastic porous media flow equation on the coarse grid using a set of pre-computed basis functions. The pre-computed basis functions are constructed based on selected realizations of the stochastic permeability field, and furthermore the solution is projected onto the finite dimensional space spanned by these basis functions. We employ multiscale methods using limited global information since the permeability fields do not have apparent scale separation. The proposed approach does not require any interpolation in stochastic space, and can easily be coupled with interpolation based approaches to predict the solution on the coarse grid. Numerical results are presented for permeability fields with Gaussian and exponential variograms.
J. E. Aarnes, Yalchin Efendiev
Added 14 Dec 2010
Updated 14 Dec 2010
Type Journal
Year 2008
Where SIAMSC
Authors J. E. Aarnes, Yalchin Efendiev
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