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.
| Author: | Philip Freese, Moritz HauckORCiDGND, Tim Keil, Daniel PeterseimORCiDGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1073071 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/107307 |
| ISSN: | 0029-599XOPAC |
| ISSN: | 0945-3245OPAC |
| Parent Title (German): | Numerische Mathematik |
| Publisher: | Springer |
| Place of publication: | Berlin |
| Type: | Article |
| Language: | English |
| Date of Publication (online): | 2023/08/31 |
| Year of first Publication: | 2024 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2023/08/31 |
| Volume: | 156 |
| First Page: | 205 |
| Last Page: | 235 |
| DOI: | https://doi.org/10.1007/s00211-023-01386-4 |
| 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 |
| Licence (German): |  CC-BY 4.0: Creative Commons: Namensnennung |
