Convergence of a Nonconforming Multiscale Finite Element Method

By Yalchin R. Efendiev, Thomas Y. Hou, Xiao-hui Wu. SIAM Journal on Numerical Analysis, 2000

324 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/7d8390b5e004a3102122938f3e00af6f4bd6fecd

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

On an energy minimizing basis for algebraic multigrid methods (2004, methodology): “Examples include RFB (residual-freebubble) method [11, 12, 13, 15] (for convection dominated problems) and the multiscale finite element methods by Hou et al [10, 14] (for numerical homogenization).”
Optimal Local Multi-scale Basis Functions for Linear Elliptic Equations with Rough Coefficient (2015, unknown): “In [21, 18, 22, 14], the authors proposed the Multi-scale ﬁnite element method (MsFEM), in which the multi-scale basis functions are constructed by solving local elliptic problems with homogeneous right hand side, and the convergence analysis of MsFEM in the periodic setting was given in [18, 15].”
Analysis of the heterogeneous multiscale method for elliptic homogenization problems (2004, background): “An alternative proposal for more general problems but with much higher cost is found in [20, 25].”
Multi-scale finite-volume method for elliptic problems in subsurface flow simulation (2003, methodology): “We also follow some principal ideas presented by Hou and Wu [8] and Efendiev et al. [ 6 ].”
Generalized Coarse Graining Procedures for Flow in Porous Media (2003, methodology): “Numerical investigations have been performed, e.g., by Hou et al. [20], Nilsen and Espendal [25], Efendiev et al. [ 15 ] or Durlovsky [12].”
On Approximation in Meshless Methods (2005, background): “Conceptually, this is the approach taken for example in [5] and [58,59,37] for calculations of very heterogeneous media.”
Navier-Stokes/Darcy Coupling: Modeling, Analysis, and Numerical Approximation (2009, methodology): “The multiscale finite element method [78, 79, 65] is an extension of an early idea of Babuška [12], which incorporates the fine scale information into the basis functions by solving the original homogeneous fine-scale differential equations on each element with proper boundary conditions.”
Multiscale Finite Element Methods for Nonlinear Problems and Their Applications (2004, background): “In particular, our studies revealed two kinds of resonance errors for nonlinear problems with the same nature as those that arise in linear problems [14].”
Removing the Cell Resonance Error in the Multiscale Finite Element Method via a Petrov-Galerkin Formulation (2004, methodology): “We continue the study of the nonconforming multiscale finite element method (MsFEM) introduced in [17, 14] for second order elliptic equations with highly oscillatory coefficients.”