@misc{10481/70927,
year = {2021},
url = {http://hdl.handle.net/10481/70927},
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 C
2 on the whole domain but fourth-order
regularity is required at vertices and C
3
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.},
organization = {Erasmus+ International Dimension programme, European Commission},
organization = {PAIDI
programme, Junta de Andalucía, Spain},
publisher = {MDPI},
keywords = {Powell–Sabin triangulation},
keywords = {Sextic Powell–Sabin splines},
keywords = {Bernstein–Bézier form},
keywords = {Marsden’s identity},
title = {Quasi-Interpolation in a Space of C 2 Sextic Splines over Powell–Sabin Triangulations},
doi = {10.3390/math9182276},
author = {Eddargani, Salah and Ibáñez Pérez, María José and Lamnii, Abdellah and Lamnii, Mohamed and Barrera Rosillo, Domingo},
}