Matrix-dependent prolongations and restrictions in a blackbox multigrid solver
Journal of Computational and Applied Mathematics
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
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
Convergence of a Nonconforming Multiscale Finite Element Method
SIAM Journal on Numerical Analysis
Multi-scale finite-volume method for elliptic problems in subsurface flow simulation
Journal of Computational Physics
Numerical methods for multiscale elliptic problems
Journal of Computational Physics
Multiscale finite-volume method for compressible multiphase flow in porous media
Journal of Computational Physics
Journal of Computational Physics
Accurate multiscale finite element methods for two-phase flow simulations
Journal of Computational Physics
Multiscale finite element methods for porous media flows and their applications
Applied Numerical Mathematics
A multilevel multiscale mimetic (M3) method for two-phase flows in porous media
Journal of Computational Physics
Upscaling methods for a class of convection-diffusion equations with highly oscillating coefficients
Journal of Computational Physics
Iterative multiscale finite-volume method
Journal of Computational Physics
Journal of Computational Physics
Modeling complex wells with the multi-scale finite-volume method
Journal of Computational Physics
Journal of Computational Physics
A multiscale cell boundary element method for elliptic problems
Applied Numerical Mathematics
Journal of Computational Physics
Applied Numerical Mathematics
Adaptive iterative multiscale finite volume method
Journal of Computational Physics
Multiscale finite element methods for high-contrast problems using local spectral basis functions
Journal of Computational Physics
An iterative multiscale finite volume algorithm converging to the exact solution
Journal of Computational Physics
A stochastic mixed finite element heterogeneous multiscale method for flow in porous media
Journal of Computational Physics
A hierarchical fracture model for the iterative multiscale finite volume method
Journal of Computational Physics
A Stochastic Mortar Mixed Finite Element Method for Flow in Porous Media with Multiple Rock Types
SIAM Journal on Scientific Computing
A new multiscale computational method for elasto-plastic analysis of heterogeneous materials
Computational Mechanics
Local-global multiscale model reduction for flows in high-contrast heterogeneous media
Journal of Computational Physics
Generalized multiscale finite element methods (GMsFEM)
Journal of Computational Physics
Ensemble level multiscale finite element and preconditioner for channelized systems and applications
Journal of Computational and Applied Mathematics
Algebraic multiscale solver for flow in heterogeneous porous media
Journal of Computational Physics
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The recently introduced multiscale finite element method for solving elliptic equations with oscillating coefficients is designed to capture the large-scale structure of the solutions without resolving all the fine-scale structures. Motivated by the numerical simulation of flow transport in highly heterogeneous porous media, we propose a mixed multiscale finite element method with an over-sampling technique for solving second order elliptic equations with rapidly oscillating coefficients. The multiscale finite element bases are constructed by locally solving Neumann boundary value problems. We provide a detailed convergence analysis of the method under the assumption that the oscillating coefficients are locally periodic. While such a simplifying assumption is not required by our method, it allows us to use homogenization theory to obtain the asymptotic structure of the solutions. Numerical experiments are carried out for flow transport in a porous medium with a random log-normal relative permeability to demonstrate the efficiency and accuracy of the proposed method.