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arXiv · 1608.04081

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

Ralf Kornhuber·Daniel Peterseim·Harry Yserentant
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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 in this paper a class of such methods that are very closely related to the method of Målqvist and Peterseim [Math. Comp. 83, 2014]. Like the method of Målqvist and Peterseim, these methods do not make explicit or implicit use of a scale separation. Their compared to that in the work of Målqvist and Peterseim strongly simplified analysis is based on a reformulation of their method in terms of variational multiscale methods and on the theory of iterative methods, more precisely, of additive Schwarz or subspace decomposition methods.

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Ralf Kornhuber, Daniel Peterseim, Harry Yserentant. 2018-01-21. An analysis of a class of variational multiscale methods based on subspace decomposition. https://doi.org/10.1090/mcom%2F3302

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