Volume 54, pp. 234-255, 2021.

Additive Schwarz preconditioners for a localized orthogonal decomposition method

Susanne C. Brenner, José C. Garay, and Li-yeng Sung


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.

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Key words

multiscale, localized orthogonal decomposition, domain decomposition, additive Schwarz

AMS subject classifications

65N12, 65N30, 65N55

Links to the cited ETNA articles

[17]Vol. 41 (2014), pp. 109-132 Ulrich Hetmaniuk and Axel Klawonn: Error estimates for a two-dimensional special finite element method based on component mode synthesis

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