A multiscale finite element method for elliptic problems in composite materials and porous media
Journal of Computational Physics
The continuous Galerkin method is locally conservative
Journal of Computational Physics
Multi-scale finite-volume method for elliptic problems in subsurface flow simulation
Journal of Computational Physics
Accurate multiscale finite element methods for two-phase flow simulations
Journal of Computational Physics
Locally Conservative Fluxes for the Continuous Galerkin Method
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
Multiscale finite element methods for high-contrast problems using local spectral basis functions
Journal of Computational Physics
Generalized multiscale finite element method. Symmetric interior penalty coupling
Journal of Computational Physics
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In this paper, we propose a method for the construction of locally conservative flux fields from Generalized Multiscale Finite Element Method (GMsFEM) pressure solutions. The flux values are obtained from an element-based postprocessing procedure in which an independent set of 4x4 linear systems need to be solved. To test the performance of the method we consider two heterogeneous permeability coefficients and couple the resulting fluxes to a two-phase flow model. The increase in accuracy associated with the computation of the GMsFEM pressure solutions is inherited by the postprocessed flux fields and saturation solutions, and is closely correlated to the size of the reduced-order systems. In particular, the addition of more basis functions to the enriched coarse space yields solutions that more accurately capture the behavior of the fine scale model. A number of numerical examples are offered to validate the performance of the method.