A STOCHASTIC MORTAR MIXED FINITE ELEMENT METHOD FOR FLOW IN POROUS MEDIA WITH MULTIPLE ROCK TYPES

作者：Ganis Benjamin^*; Yotov Ivan; Zhong Ming

来源：SIAM Journal on Scientific Computing, 2011, 33(3): 1439-1474.

DOI：10.1137/100790689

• uncertainty quantification
• stochastic collocation
• multiscale basis
• mortar finite element
• mixed finite element
• porous media flow
• Smolyak sparse grid

This paper presents an efficient multiscale stochastic framework for uncertainty quantification in modeling of flow through porous media with multiple rock types. The governing equations are based on Darcy's law with nonstationary stochastic permeability represented as a sum of local Karhunen-Loeve expansions. The approximation uses stochastic collocation on either a tensor product or a sparse grid, coupled with a domain decomposition algorithm known as the multiscale mortar mixed finite element method. The latter method requires solving a coarse scale mortar interface problem via an iterative procedure. The traditional implementation requires the solution of local fine scale linear systems on each iteration. We employ a recently developed modification of this method that precomputes a multiscale flux basis to avoid the need for subdomain solves on each iteration. In the stochastic setting, the basis is further reused over multiple realizations, leading to collocation algorithms that are more efficient than the traditional implementation by orders of magnitude. Error analysis and numerical experiments are presented.

• 出版日期2011