A Generalized Framework for Higher-Order Localized Orthogonal Decomposition Methods
Numerical Analysis
2025-06-25 v1 Numerical Analysis
Abstract
We introduce a generalized framework for studying higher-order versions of the multiscale method known as Localized Orthogonal Decomposition. Through a suitable reformulation, we are able to accommodate both conforming and nonconforming constraints in the construction process. In particular, we offer a new perspective on localization strategies. We fully analyze the strategy for linear elliptic problems and discuss extensions to the Helmholtz equation and the Gross--Pitaevskii eigenvalue problem. Numerical examples are presented that particularly provide valuable comparisons between conforming and nonconforming constraints.
Cite
@article{arxiv.2506.19462,
title = {A Generalized Framework for Higher-Order Localized Orthogonal Decomposition Methods},
author = {Moritz Hauck and Alexei Lozinski and Roland Maier},
journal= {arXiv preprint arXiv:2506.19462},
year = {2025}
}
Comments
23 pages, 5 figures