Special finite element methods for a class of second order elliptic problems with rough coefficients
SIAM Journal on Numerical Analysis
A multiscale finite element method for elliptic problems in composite materials and porous media
Journal of Computational Physics
Homogenization via p-FEM for problems with microstructure
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
A mixed multiscale finite element method for elliptic problems with oscillating coefficients
Mathematics of Computation
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Preconditioning Markov Chain Monte Carlo Simulations Using Coarse-Scale Models
SIAM Journal on Scientific Computing
Coarse-gradient Langevin algorithms for dynamic data integration and uncertainty quantification
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Accurate multiscale finite element methods for two-phase flow simulations
Journal of Computational Physics
Robust solvers for symmetric positive definite operators and weighted poincaré inequalities
LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
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In this paper, we discuss some applications of multiscale finite element methods to two-phase immiscible flow simulations in heterogeneous porous media. We discuss some extensions of multiscale finite element methods which take into account limited global information. These methods are well suited for channelized porous media, where the long-range effects are important. This is typical for some recent benchmark tests, such as the SPE comparative solution project [M. Christie, M. Blunt, Tenth SPE comparative solution project: A comparison of upscaling techniques, SPE Reser. Eval. Engrg. 4 (2001) 308-317], where porous media has a channelized structure. The applications of multiscale finite element methods to inverse problems arisen in subsurface characterization are also discussed in the paper.