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BIT Numerical Mathematics

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01.03.2013

Error bounds on the approximation of functions and partial derivatives by quadratic spline quasi-interpolants on non-uniform criss-cross triangulations of a rectangular domain

verfasst von: Catterina Dagnino, Sara Remogna, Paul Sablonnière

Erschienen in: BIT Numerical Mathematics | Ausgabe 1/2013

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Abstract

Given a non-uniform criss-cross triangulation of a rectangular domain Ω, we consider the approximation of a function f and its partial derivatives, by general C ¹ quadratic spline quasi-interpolants and their derivatives. We give error bounds in terms of the smoothness of f and the characteristics of the triangulation. Then, the preceding theoretical results are compared with similar results in the literature. Finally, several examples are proposed for illustrating various applications of the quasi-interpolants studied in the paper.

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Titel: Error bounds on the approximation of functions and partial derivatives by quadratic spline quasi-interpolants on non-uniform criss-cross triangulations of a rectangular domain
verfasst von: Catterina Dagnino
Sara Remogna
Paul Sablonnière
Publikationsdatum: 01.03.2013
Verlag: Springer Netherlands
Erschienen in: BIT Numerical Mathematics / Ausgabe 1/2013
Print ISSN: 0006-3835
Elektronische ISSN: 1572-9125
DOI: https://doi.org/10.1007/s10543-012-0392-2

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