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ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis, pp. 234-255, 2021/03/16
We investigate a variant of the localized orthogonal decomposition method (Henning and Peterseim, [Multiscale Model. Simul., 11 (2013), pp. 1149–1175] and Målqvist and Peterseim, [Math. Comp., 83 (2014), pp. 2583–2603]) for elliptic problems with rough coefficients. The construction of the basis of the multiscale finite element space is based on domain decomposition techniques, which is motivated by the recent work of Kornhuber, Peterseim, and Yserentant [Math. Comp., 87 (2018), pp. 2765–2774]. We also design and analyze additive Schwarz domain decomposition preconditioners for the resulting discrete problems.
Keywords: multiscale, localized orthogonal decomposition, domain decomposition, additive Schwarz