A super-localized generalized finite element method

  • 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.

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Author:Philip Freese, Moritz HauckORCiDGND, Tim Keil, Daniel PeterseimORCiDGND
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/107307
Parent Title (German):Numerische Mathematik
Place of publication:Berlin
Year of first Publication:2023
Publishing Institution:Universität Augsburg
Release Date:2023/08/31
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
Latest Publications (not yet published in print):Aktuelle Publikationen (noch nicht gedruckt erschienen)
Licence (German):CC-BY 4.0: Creative Commons: Namensnennung (mit Print on Demand)