On the Use of a Mixed Multiscale Finite Element Method for GreaterFlexibility and Increased Speed or Improved Accuracy in Reservoir Simulation

By Jørg E. Aarnes. Multiscale Modeling & simulation, 2004

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Multiscale mixed/mimetic methods on corner-point grids (2008, methodology): “Indeed, for two-phase flow simulations, where the pressure equation needs to be solved repeatedly, it has been demonstrated that the basis functions need to be computed only once, or updated infrequently [1, 22, 24].”
A Multiscale Mortar Mixed Finite Element Method (2007, methodology): “, [7, 18, 3, 1, 4, 2] and the related control volume work [33]).”
Generalized multiscale finite element methods (GMsFEM) (2013, background): “, see [40, 43, 1, 3, 4, 7, 8, 20, 21, 33, 42] for upscaling and multiscale methods) attempt to approximate the solution in local (coarse-grid) regions for all input parameters without computing global snapshots of solutions.”
Domain Decomposition Preconditioners for Multiscale Flows in High Contrast Media: Reduced Dimension Coarse Spaces (2010, unknown): “It is common to use upscaled or multiscale models to solve flow and transport processes on the coarse grid [1, 2, 4, 5, 6, 7, 8, 11, 23].”