A super-localized generalized finite element method
Artikel i vetenskaplig tidskrift, 2024

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.

Författare

Philip Freese

Technische Universität Hamburg-Harburg (TUHH)

Moritz Hauck

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Tim Keil

Universität Münster

Daniel Peterseim

Universität Augsburg

Numerische Mathematik

0029-599X (ISSN) 0945-3245 (eISSN)

Vol. 156 1 205-235

Ämneskategorier

Beräkningsmatematik

DOI

10.1007/s00211-023-01386-4

Mer information

Senast uppdaterat

2024-03-07