An improved high-order method for elliptic multiscale problems
- 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 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 (2021), pp. 1067–1089]. 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.
Author: | Zhaonan Dong, Moritz HauckORCiDGND, Roland Maier |
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Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/108721 |
ISSN: | 0036-1429OPAC |
Parent Title (English): | Siam Journal on Numerical Analysis |
Publisher: | Society for Industrial & Applied Mathematics (SIAM) |
Type: | Article |
Language: | English |
Date of first Publication: | 2023/07/27 |
Release Date: | 2023/10/26 |
Tag: | Multiscale Method; Numerical Homogenization; High-order Method; Localization |
Volume: | 61 |
Issue: | 4 |
First Page: | 1918 |
Last Page: | 1937 |
DOI: | https://doi.org/10.1137/22M153392X |
Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik | |
Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |