A super-localized generalized finite element method.

Autor:	Freese, Philip, Hauck, Moritz, Keil, Tim, Peterseim, Daniel
Předmět:	FINITE element method ELLIPTIC differential equations ALGEBRAIC spaces ORTHOGONAL decompositions UNIFORM spaces A posteriori error analysis
Zdroj:	Numerische Mathematik; Feb2024, Vol. 156 Issue 1, p205-235, 31p
Abstrakt:	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. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
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