Numerical Subgrid Upscaling of Two-Phase Flow in Porous Media

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A comparison of multiscale methods for elliptic problems in porous media flow (2008, methodology): “here follow [5, 6] and let the coarse-scale approximation space be the BDM1 space.”
Multi-scale finite-volume method for elliptic problems in subsurface flow simulation (2003, methodology): “Arbogast [ 1 ] and Arbogast and Bryant [2] presented a mixed finite-element method, where the fine-scale effects are localized by a boundary condition assumption at the coarse element boundaries.”
Multiscale mixed/mimetic methods on corner-point grids (2008, background): “We note that MsMFEM is related to subgrid upscaling introduced by Arbogast [10, 7, 8].”
Implementation of a Locally Conservative Numerical Subgrid Upscaling Scheme for Two-Phase Darcy Flow (2002, methodology): “In [6] and [ 3 ] a new approach to upscaling an elliptic partial differential equation was introduced that involves the decomposition of the solution operator into two pieces.”