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zbMATH Open
Article . 2004
Data sources: zbMATH Open
Multiscale Modeling and Simulation
Article . 2004 . Peer-reviewed
Data sources: Crossref
DBLP
Article . 2020
Data sources: DBLP
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Numerical Homogenization of Nonlinear Random Parabolic Operators

Numerical homogenization of nonlinear random parabolic operators
Authors: Yalchin Efendiev; Alexander Pankov;

Numerical Homogenization of Nonlinear Random Parabolic Operators

Abstract

Summary: We study the numerical homogenization of nonlinear random parabolic equations. This procedure is developed within a finite element framework. A careful choice of multiscale finite element bases and the global formulation of the problem on the coarse grid allow us to prove the convergence of the numerical method to the homogenized solution of the equation. The relation of the proposed numerical homogenization procedure to multiscale finite element methods is discussed. Within our numerical procedure one is able to approximate the gradients of the solutions. To show this feature of our method we develop numerical correctors that contain two scales, the numerical and the physical. Finally, we would like to note that our numerical homogenization procedure can be used for the general type of heterogeneities.

Related Organizations
Keywords

upscaling, multiscale, Homogenization applied to problems in fluid mechanics, finite element, homogenization, Nonlinear parabolic equations, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, Homogenization and oscillations in dynamical problems of solid mechanics, Homogenization in context of PDEs; PDEs in media with periodic structure, random nonlinear parabolic operators

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
68
Top 10%
Top 10%
Top 10%
bronze