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


Authors: Ralf Kornhuber, Daniel Peterseim and Harry Yserentant
Journal: Math. Comp. 87 (2018), 2765-2774
MSC (2010): Primary 65N12, 65N30, 65N55
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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Additional Information

Ralf Kornhuber
Affiliation: Institut für Mathematik, Freie Universität Berlin, 14195 Berlin, Germany
Email: kornhuber@math.fu-berlin.de

Daniel Peterseim
Affiliation: Institut für Mathematik, Universität Augsburg, 86135 Augsburg, Germany
Email: daniel.peterseim@math.uni-augsburg.de

Harry Yserentant
Affiliation: Institut für Mathematik, Technische Universität Berlin, 10623 Berlin, Germany
Email: yserentant@math.tu-berlin.de

DOI: https://doi.org/10.1090/mcom/3302
Received by editor(s): November 22, 2016
Received by editor(s) in revised form: May 6, 2017
Published electronically: January 19, 2018
Additional Notes: This research was supported by Deutsche Forschungsgemeinschaft through SFB 1114
Article copyright: © Copyright 2018 American Mathematical Society

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