An analysis of a class of variational multiscale methods based on subspace decomposition

Kornhuber, Ralf; Peterseim, Daniel; Yserentant, Harry

doi:10.1090/mcom/3302

An analysis of a class of variational multiscale methods based on subspace decomposition
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by Ralf Kornhuber, Daniel Peterseim and Harry Yserentant;

Math. Comp. 87 (2018), 2765-2774

DOI: https://doi.org/10.1090/mcom/3302

Published electronically: January 19, 2018

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Abstract:

Numerical homogenization tries to approximate the solutions of elliptic partial differential equations with strongly oscillating coefficients by functions from modified finite element spaces. We present a class of such methods that are closely related to the methods that have recently been proposed by Målqvist and Peterseim [Math. Comp. 83, 2014, pp. 2583–2603]. Like these methods, the new methods do not make explicit or implicit use of a scale separation. Their comparatively simple analysis is based on the theory of additive Schwarz or subspace decomposition methods.

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