Contrast Independent Localization of Multiscale Problems
Journal article, 2017

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.

high contrast coefficient

multiscale

numerical homogenization

Author

F. Hellman

Uppsala University

Axel Målqvist

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University of Gothenburg

Multiscale Modeling and Simulation

1540-3459 (ISSN)

Vol. 15 4 1325-1355

Subject Categories

Mathematics

DOI

10.1137/16M1100460

More information

Latest update

4/11/2018