Functional a posteriori estimates for the fractional Laplacian problem
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911398664077312 |
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| author | Nazarov, Alexander Repin, Sergey |
| author_facet | Nazarov, Alexander Repin, Sergey |
| contents | The paper is concerned with a posteriori estimates for approximations of boundary value problems generated by the spectral fractional Laplace operator. The derivation is based upon the Stinga--Torrea extension, which generalizes the Caffarelli--Silvestre extension and transfers the corresponding nonlocal problem in a bounded domain to a local problem of higher dimensionality. A posteriori estimates are first derived for this local problem. Two-sided error bounds for the original problem follow from them. The estimates are fully computable and contain no conditions and constants depending on a method or mesh used to compute an approximation. They are valid for any energy admissible approximation of the extended problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12664 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Functional a posteriori estimates for the fractional Laplacian problem Nazarov, Alexander Repin, Sergey Analysis of PDEs 35R11, 65N99 The paper is concerned with a posteriori estimates for approximations of boundary value problems generated by the spectral fractional Laplace operator. The derivation is based upon the Stinga--Torrea extension, which generalizes the Caffarelli--Silvestre extension and transfers the corresponding nonlocal problem in a bounded domain to a local problem of higher dimensionality. A posteriori estimates are first derived for this local problem. Two-sided error bounds for the original problem follow from them. The estimates are fully computable and contain no conditions and constants depending on a method or mesh used to compute an approximation. They are valid for any energy admissible approximation of the extended problem. |
| title | Functional a posteriori estimates for the fractional Laplacian problem |
| topic | Analysis of PDEs 35R11, 65N99 |
| url | https://arxiv.org/abs/2510.12664 |