NDLI: Quasi-Interpolation in a Space of $C^{2}$ Sextic Splines over Powell

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Quasi-Interpolation in a Space of $C^{2}$ Sextic Splines over Powell–Sabin Triangulations

Content Provider	MDPI
Author	Mar, ía José Ibáñez Eddargani, Salah Lamnii, Abdellah Lamnii, Mohamed Barrera, Domingo
Copyright Year	2021
Description	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.
Starting Page	2276
e-ISSN	22277390
DOI	10.3390/math9182276
Journal	Mathematics
Issue Number	18
Volume Number	9
Language	English
Publisher	MDPI
Publisher Date	2021-09-16
Access Restriction	Open
Subject Keyword	Mathematics Industrial Engineering Powell–sabin Triangulation Sextic Powell–sabin Splines Bernstein–bézier Form Marsden's Identity
Content Type	Text
Resource Type	Article

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