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A super-localized generalized finite element method
Citation Link: https://doi.org/10.15480/882.9009
Publikationstyp
Journal Article
Date Issued
2024-02
Sprache
English
Author(s)
TORE-DOI
Journal
Volume
156
Issue
1
Start Page
205
End Page
235
Citation
Numerische Mathematik 156 (1): 205-235 (2024-02)
Publisher DOI
Scopus ID
Publisher
Springer
This paper presents a novel multi-scale method for elliptic partial differential equations with arbitrarily rough coefficients. In the spirit of numerical homogenization, the method constructs problem-adapted ansatz spaces with uniform algebraic approximation rates. Localized basis functions with the same super-exponential localization properties as the recently proposed Super-Localized Orthogonal Decomposition enable an efficient implementation. The method’s basis stability is enforced using a partition of unity approach. A natural extension to higher order is presented, resulting in higher approximation rates and enhanced localization properties. We perform a rigorous a priori and a posteriori error analysis and confirm our theoretical findings in a series of numerical experiments. In particular, we demonstrate the method’s applicability for challenging high-contrast channeled coefficients.
Subjects
65N12
65N30
DDC Class
510: Mathematics
Publication version
publishedVersion
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s00211-023-01386-4.pdf
Type
Main Article
Size
842.33 KB
Format
Adobe PDF