High-order numerical integration on self-affine sets
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908709644402688 |
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| author | Joly, Patrick Kachanovska, Maryna Moitier, Zoïs |
| author_facet | Joly, Patrick Kachanovska, Maryna Moitier, Zoïs |
| contents | We construct an interpolatory high-order cubature rule to compute integrals of smooth functions over self-affine sets with respect to an invariant measure. The main difficulty is the computation of the cubature weights, which we characterize algebraically, by exploiting a self-similarity property of the integral. We propose an $h$-version and a $p$-version of the cubature, present an error analysis and conduct numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00637 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | High-order numerical integration on self-affine sets Joly, Patrick Kachanovska, Maryna Moitier, Zoïs Numerical Analysis 65D30, 65D32, 28A80 We construct an interpolatory high-order cubature rule to compute integrals of smooth functions over self-affine sets with respect to an invariant measure. The main difficulty is the computation of the cubature weights, which we characterize algebraically, by exploiting a self-similarity property of the integral. We propose an $h$-version and a $p$-version of the cubature, present an error analysis and conduct numerical experiments. |
| title | High-order numerical integration on self-affine sets |
| topic | Numerical Analysis 65D30, 65D32, 28A80 |
| url | https://arxiv.org/abs/2410.00637 |