Simultaneous spatial-parametric collocation approximation for parametric PDEs with log-normal random inputs
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914426131578880 |
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| author | Dũng, Dinh |
| author_facet | Dũng, Dinh |
| contents | We establish convergence rates for a fully discrete, multi-level, linear collocation method solving parametric elliptic PDEs on bounded polygonal domains with log-normal inputs. The method uses a finite set of function evaluations in the spatial-parametric domain. Compared with the best-known fully discrete collocation rates, these rates are significantly improved and, up to logarithmic factors, match the rates of best n-term approximations. The results follow from applying general multi-level linear sampling recovery theory in abstract Bochner spaces -- via extended least-squares -- to infinite-dimensional holomorphic functions. The abstract multi-level recovery in Bochner spaces guarantees yield the improved rates when specialized to the parametric PDE setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07799 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simultaneous spatial-parametric collocation approximation for parametric PDEs with log-normal random inputs Dũng, Dinh Numerical Analysis 65C30, 65N15, 65N35, 41A25, 41A65 We establish convergence rates for a fully discrete, multi-level, linear collocation method solving parametric elliptic PDEs on bounded polygonal domains with log-normal inputs. The method uses a finite set of function evaluations in the spatial-parametric domain. Compared with the best-known fully discrete collocation rates, these rates are significantly improved and, up to logarithmic factors, match the rates of best n-term approximations. The results follow from applying general multi-level linear sampling recovery theory in abstract Bochner spaces -- via extended least-squares -- to infinite-dimensional holomorphic functions. The abstract multi-level recovery in Bochner spaces guarantees yield the improved rates when specialized to the parametric PDE setting. |
| title | Simultaneous spatial-parametric collocation approximation for parametric PDEs with log-normal random inputs |
| topic | Numerical Analysis 65C30, 65N15, 65N35, 41A25, 41A65 |
| url | https://arxiv.org/abs/2502.07799 |