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arXiv · 2506.19462

A Generalized Framework for Higher-Order Localized Orthogonal Decomposition Methods

Moritz Hauck·Alexei Lozinski·Roland Maier
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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.

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Moritz Hauck, Alexei Lozinski, Roland Maier. 2025-06-24. A Generalized Framework for Higher-Order Localized Orthogonal Decomposition Methods. https://arxiv.org/abs/2506.19462

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