Multiscale mixed/mimetic methods on corner-point grids

By Jørg E. Aarnes, Stein Krogstad, Knut-Andreas Lie. 2008

175 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/5e4e8e3146970fb47f9b7828d7533679b9cc87e0

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Basic principles of Virtual Element Methods (2013, methodology): “In their last presentation they could be considered as a form of approximations either by means of Cochains, or by Finite Element methods in which only the degrees of freedom are used (since the trial functions are not available in the interior of the elements)[31, 19, 1, 21].”
Virtual Elements for Linear Elasticity Problems (2013, background): “(For a partial list of citations we refer to [29, 25, 17, 24, 26, 13, 15, 8, 27, 1, 14, 6, 18, 21, 32, 11, 2, 10, 16].”
Equivalent projectors for virtual element methods (2013, methodology): “In their more recent evolution Mimetic Finite Differences (MFD) were often presented either as a form of Cochain approximation or as a sort of Finite Element methods in which only the degrees of freedom are used (and, in principle, there are no test and trial functions attached to them) [33, 19, 1, ”
Mimetic finite difference method (2014, background): “…and application of the mimetic discretizations have been done in various research groups in Europe and US: subsurface flows on corner-point meshes, [1]; development of mimetic discretizations based on a discrete calculus for fluid dynamics [154] [222] [249], geophysical flows, [4] [45] [224]…”
A comparison of multiscale methods for elliptic problems in porous media flow (2008, methodology): “For unstructured meshes, meshes with non-matching faces or meshes with complex cell geometries, we claim that MsMFEM is significantly less complicated to implement (see e.g., [ 3 ] for implementations of MsMFEM on corner-point grids).”
Open-source MATLAB implementation of consistent discretisations on complex grids (2012, methodology): “However, we neglect gravity and instead of assuming a homogeneous permeability, we increase the number of cells in the vertical direction to 20, impose a log-normal, layered permeability as shown in Figure 3, and use the layering from the permeability to determine the extent of the coarse blocks; a ”