We investigate the construction of local quasi-interpolation schemes based on a family of bivariate spline functions with smoothness r≥1 and polynomial degree 3r−1. These splines are defined on triangulations with Powell-Sabin refinement, and they can be represented in terms of locally supported basis functions that form a convex partition of unity. With the aid of the blossoming technique, we first derive a Marsden-like identity representing polynomials of degree 3r−1 in such a spline form. Then we present a general recipe to construct various families of smooth quasi-interpolation schemes involving values and/or derivatives of a given function.

Speleers, H. (2015). A Family of Smooth Quasi-interpolants Defined Over Powell–Sabin Triangulations. CONSTRUCTIVE APPROXIMATION, 41(2), 297-324 [10.1007/s00365-014-9248-0].

A Family of Smooth Quasi-interpolants Defined Over Powell–Sabin Triangulations

Speleers H.
2015-04-01

Abstract

We investigate the construction of local quasi-interpolation schemes based on a family of bivariate spline functions with smoothness r≥1 and polynomial degree 3r−1. These splines are defined on triangulations with Powell-Sabin refinement, and they can be represented in terms of locally supported basis functions that form a convex partition of unity. With the aid of the blossoming technique, we first derive a Marsden-like identity representing polynomials of degree 3r−1 in such a spline form. Then we present a general recipe to construct various families of smooth quasi-interpolation schemes involving values and/or derivatives of a given function.
apr-2015
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/08 - ANALISI NUMERICA
English
Con Impact Factor ISI
Smooth Powell-Sabin splines; Normalized B-splines; Macro-elements; Marsden-like identity; Quasi-interpolation
Speleers, H. (2015). A Family of Smooth Quasi-interpolants Defined Over Powell–Sabin Triangulations. CONSTRUCTIVE APPROXIMATION, 41(2), 297-324 [10.1007/s00365-014-9248-0].
Speleers, H
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/215153
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