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Mathematics > Numerical Analysis

arXiv:2211.02484 (math)
[Submitted on 4 Nov 2022 (v1), last revised 17 Apr 2023 (this version, v2)]

Title:An improved high-order method for elliptic multiscale problems

Authors:Zhaonan Dong, Moritz Hauck, Roland Maier
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Abstract:In this work, we propose a high-order multiscale method for an elliptic model problem with rough and possibly highly oscillatory coefficients. Convergence rates of higher order are obtained using the regularity of the right-hand side only. Hence, no restrictive assumptions on the coefficient, the domain, or the exact solution are required. In the spirit of the Localized Orthogonal Decomposition, the method constructs coarse problem-adapted ansatz spaces by solving auxiliary problems on local subdomains. More precisely, our approach is based on the strategy presented by Maier [SIAM J. Numer. Anal. 59(2), 2021]. The unique selling point of the proposed method is an improved localization strategy curing the effect of deteriorating errors with respect to the mesh size when the local subdomains are not large enough. We present a rigorous a priori error analysis and demonstrate the performance of the method in a series of numerical experiments.
Comments: 22 pages, 6 figures
Subjects: Numerical Analysis (math.NA)
MSC classes: 65N12, 65N30
Cite as: arXiv:2211.02484 [math.NA]
  (or arXiv:2211.02484v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2211.02484

Submission history

From: Moritz Hauck [view email]
[v1] Fri, 4 Nov 2022 14:21:21 UTC (638 KB)
[v2] Mon, 17 Apr 2023 13:05:18 UTC (831 KB)
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