Quasi-Interpolation in a Space of C2 Sextic Splines over Powell–Sabin Triangulations

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...

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Bibliographic Details
Published inMathematics (Basel) Vol. 9; no. 18; p. 2276
Main Authors Eddargani, Salah, Ibáñez, María José, Lamnii, Abdellah, Lamnii, Mohamed, Barrera, Domingo
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 16.09.2021
Subjects
Algorithms
Apexes
Approximation
Bernstein–Bézier form
Graph theory
Interpolation
Marsden’s identity
Mathematical analysis
Mathematics
Operators
Partial differential equations
Polynomials
Powell–Sabin triangulation
Regularity
sextic Powell–Sabin splines
Spline functions
Triangulation
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math9182276