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

Kornhuber, R. and Peterseim, D. and Yserentant, H. (2018) An analysis of a class of variational multiscale methods based on subspace decomposition. Mathematics of Computation . ISSN 1088-6842 (online)

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Official URL: http://dx.doi.org/10.1090/mcom/3302

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 M{\aa}lqvist and Peterseim [Math. Comp. 83, 2014]. Like the method of M{\aa}lqvist and Peterseim, these methods do not make explicit or implicit use of a scale separation. Their compared to that in the work of M{\aa}lqvist 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.

Item Type:Article
Additional Information:SFB 1114 Preprint in arXiv:1608.04081
Subjects:Mathematical and Computer Sciences > Mathematics > Numerical Analysis
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2063
Deposited By: Ekaterina Engel
Deposited On:03 Apr 2017 10:02
Last Modified:24 Jan 2018 11:18

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