| Issue |
ESAIM: M2AN
Volume 60, Number 1, January-February 2026
|
|
|---|---|---|
| Page(s) | 445 - 471 | |
| DOI | https://doi.org/10.1051/m2an/2026006 | |
| Published online | 11 March 2026 | |
A generalized framework for higher-order Localized Orthogonal Decomposition methods
1
Institute for Applied and Numerical Mathematics, Karlsruhe Institute of Technology, Englerstr. 2, 76131 Karlsruhe, Germany
2
Université Marie et Louis Pasteur, CNRS, LmB (UMR 6623), F-25000 Besançon, France
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
30
July
2025
Accepted:
13
January
2026
Abstract
We revisit the higher-order Localized Orthogonal Decomposition variant by Maier [SIAM J. Numer. Anal. 59 (2021) 1067–1089] based on nonconforming constraints (discontinuous finite element spaces) and introduce a new variant based on conforming constraints (continuous finite elements), putting both approaches in a general unified framework. We propose a new localization strategy that is suitable for both approaches and offers a new perspective on the localization of LOD in general. We fully analyze the strategy for linear scalar elliptic problems and discuss extensions to the Helmholtz equation and the Gross–Pitaevskii eigenvalue problem. Numerical examples are presented that provide valuable comparisons between conforming and nonconforming constraints.
Mathematics Subject Classification: 65N12 / 65N15 / 65N30
Key words: Multiscale method / localized orthogonal decomposition / higher-order / a priori error analysis / exponential decay
© The authors. Published by EDP Sciences, SMAI 2026
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