A mixed multiscale finite element method for elliptic problems with oscillating coefficients

By Zhiming Chen, Thomas Y. Hou. Mathematics of Computation, 2003

492 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/9d698a68c8792d1d3e1bc368b9774d0e2e456eec

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Optimal Local Multi-scale Basis Functions for Linear Elliptic Equations with Rough Coefficient (2015, unknown): “Consider a set of basis functions”
A Multiscale Mortar Mixed Finite Element Method (2007, methodology): “, [7, 18, 3, 1, 4, 2] and the related control volume work [33]).”
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].”
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.”
Open-source MATLAB implementation of consistent discretisations on complex grids (2012, methodology): “In the multiscale mixed finite-element (MsMFE) method [4, 11], the coarse-scale degrees of freedom are associated with faces in the coarse grid (coarse-grid fluxes) and the reconstruction operator is associated with the fluxes and is defined by solving flow problems on a primal coarse grid.”
A Multiscale Restriction-Smoothed Basis Method for Compressible Black-Oil Models (2016, methodology): “On the other hand, the multiscale mixed finite-element (MsMFE) method [10] is the method that has come the longest way in incorporating realistic descriptions of reservoir geology, see [1–3, 42, 46].”
A comparison of multiscale methods for elliptic problems in porous media flow (2008, methodology): “The purpose of this paper is to compare and validate three selected multiscale methods in terms of accuracy, robustness, and computational complexity; a mixed multiscale finite-element method [13, 1], a two-scale conservative subgrid approach [5, 6], and a multiscale finitevolume method [25, 24].”
Multiscale mixed/mimetic methods on corner-point grids (2008, background): “The multiscale mixed finite-element formulation [16, 1, 3] has previously proved to be a particularly versatile approach for flow simulation on Cartesian grids in the sense that it produces more accurate and robust results than what is obtained by traditional upscaling approaches; see [2].”