We investigate a variant of the localized orthogonal decomposition method (Henning and Peterseim, [Multiscale Model. Simul., 11 (2013), pp. 1149 1175] and Malqvist 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.
Publication Source (Journal or Book title)
Electronic Transactions on Numerical Analysis
Brenner, S., Garay, J., & Sung, L. (2020). Additive schwarz preconditioners for a localized orthogonal decomposition method. Electronic Transactions on Numerical Analysis, 54, 234-255. https://doi.org/10.1553/ETNA_VOL54S234