A Generalized Framework for Higher-Order Localized Orthogonal Decomposition Methods
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915357564862464 |
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| author | Hauck, Moritz Lozinski, Alexei Maier, Roland |
| author_facet | Hauck, Moritz Lozinski, Alexei Maier, Roland |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_19462 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Generalized Framework for Higher-Order Localized Orthogonal Decomposition Methods Hauck, Moritz Lozinski, Alexei Maier, Roland Numerical Analysis 65N12, 65N15, 65N30 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. |
| title | A Generalized Framework for Higher-Order Localized Orthogonal Decomposition Methods |
| topic | Numerical Analysis 65N12, 65N15, 65N30 |
| url | https://arxiv.org/abs/2506.19462 |