Mixed multiscale finite element methods for stochastic porous media flows

J. E. Aarnes, Y. Efendiev

Research output: Contribution to journalArticlepeer-review

70 Scopus citations


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 precomputed basis functions. The precomputed 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 normal and exponential variograms.

Original languageEnglish (US)
Pages (from-to)2319-2339
Number of pages21
JournalSIAM Journal on Scientific Computing
Issue number5
StatePublished - 2007
Externally publishedYes


  • Finite element
  • Multiscale
  • Porous media
  • Stochastic

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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