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Contrast Independent Localization of Multiscale Problems

Journal article
Authors F. Hellman
Axel Målqvist
Published in Multiscale Modeling & Simulation
Volume 15
Issue 4
Pages 1325-1355
ISSN 1540-3459
Publication year 2017
Published at Department of Mathematical Sciences
Pages 1325-1355
Language en
Keywords high contrast coefficient, multiscale, numerical homogenization, boundary-value-problems, finite-element-method, elliptic problems, approximation, coefficients, Mathematics, Physics
Subject categories Mathematical physics, Mathematics


The accuracy of many multiscale methods based on localized computations suffers from high contrast coefficients since the localization error generally depends on the contrast. We study a class of methods based on the variational multiscale method, where the range and kernel of a quasi-interpolation operator de fines the method. We present a novel interpolation operator for two-valued coefficients and prove that it yields contrast independent localization error under physically justified assumptions on the geometry of inclusions and channel structures in the coefficient. The idea developed in the paper can be transferred to more general operators and our numerical experiments show that the contrast independent localization property follows.

Page Manager: Webmaster|Last update: 9/11/2012

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