| Autor: |
Eddargani, Salah, Manni, Carla, Speleers, Hendrik |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
In this paper, we identify families of quadrature rules that are exact for sufficiently smooth spline spaces on uniformly refined triangles in $\mathbb{R}^2$. Given any symmetric quadrature rule on a triangle $T$ that is exact for polynomials of a specific degree $d$, we investigate if it remains exact for sufficiently smooth splines of the same degree $d$ defined on the Clough-Tocher 3-split or the (uniform) Powell-Sabin 6-split of $T$. We show that this is always true for $C^{2r-1}$ splines having degree $d=3r$ on the former split or $d=2r$ on the latter split, for any positive integer $r$. Our analysis is based on the representation of the considered spline spaces in terms of suitable simplex splines. |
| Databáze: |
arXiv |
| Externí odkaz: |
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