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Keywords = Powell–Sabin triangulation

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22 pages, 1850 KB  
Article
Quasi-Interpolation in a Space of C2 Sextic Splines over Powell–Sabin Triangulations
by Salah Eddargani, María José Ibáñez, Abdellah Lamnii, Mohamed Lamnii and Domingo Barrera
Mathematics 2021, 9(18), 2276; https://doi.org/10.3390/math9182276 - 16 Sep 2021
Cited by 5 | Viewed by 2135
Abstract
In this work, we study quasi-interpolation in a space of sextic splines defined over Powell–Sabin triangulations. These spline functions are of class C2 on the whole domain but fourth-order regularity is required at vertices and C3 regularity is imposed across the [...] Read more.
In this work, we study quasi-interpolation in a space of sextic splines defined over Powell–Sabin triangulations. These spline functions are of class C2 on the whole domain but fourth-order regularity is required at vertices and C3 regularity is imposed across the edges of the refined triangulation and also at the interior point chosen to define the refinement. An algorithm is proposed to define the Powell–Sabin triangles with a small area and diameter needed to construct a normalized basis. Quasi-interpolation operators which reproduce sextic polynomials are constructed after deriving Marsden’s identity from a more explicit version of the control polynomials introduced some years ago in the literature. Finally, some tests show the good performance of these operators. Full article
(This article belongs to the Section E: Applied Mathematics)
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