Adaptive refinement for eigenvalue problems based on an associated source problem
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915316462780416 |
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| author | Giani, Stefano Ovall, Jeffrey Pinochet-Soto, Gabriel |
| author_facet | Giani, Stefano Ovall, Jeffrey Pinochet-Soto, Gabriel |
| contents | We introduce an adaptive finite element scheme for the efficient approximation of a (large) collection of eigenpairs of selfadjoint elliptic operators in which the adaptive refinement is driven by the solution of a single source problem -- the so-called landscape problem for the operator -- instead of refining based on the computed eigenpairs. Some theoretical justification for the approach is provided, and extensive empirical results indicate that it can provide an attractive alternative to standard adaptive schemes, particularly in the hp-adaptive environment. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05311 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adaptive refinement for eigenvalue problems based on an associated source problem Giani, Stefano Ovall, Jeffrey Pinochet-Soto, Gabriel Numerical Analysis 65N25, 65N30, 65N50 We introduce an adaptive finite element scheme for the efficient approximation of a (large) collection of eigenpairs of selfadjoint elliptic operators in which the adaptive refinement is driven by the solution of a single source problem -- the so-called landscape problem for the operator -- instead of refining based on the computed eigenpairs. Some theoretical justification for the approach is provided, and extensive empirical results indicate that it can provide an attractive alternative to standard adaptive schemes, particularly in the hp-adaptive environment. |
| title | Adaptive refinement for eigenvalue problems based on an associated source problem |
| topic | Numerical Analysis 65N25, 65N30, 65N50 |
| url | https://arxiv.org/abs/2501.05311 |