Interpolation operators on a triangle with one curved side

We construct certain Lagrange, Hermite and Birkhoff-type operators, which interpolate a given function and some of its derivatives on the border of a triangle with one curved side, as well as some of their product and Boolean sum operators. We study the interpolation properties and the order of accu...

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Veröffentlicht in:	BIT (Nordisk Tidskrift for Informationsbehandling) 2010-06, Vol.50 (2), p.243-267
Hauptverfasser:	Coman, Gheorghe, Cătinaş, Teodora
Format:	Artikel
Sprache:	eng
Schlagworte:	Approximations and expansions Computational Mathematics and Numerical Analysis Exact sciences and technology Mathematical analysis Mathematics Mathematics and Statistics Numeric Computing Numerical analysis Numerical analysis. Scientific computation Numerical approximation Sciences and techniques of general use
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Beschreibung
Zusammenfassung:	We construct certain Lagrange, Hermite and Birkhoff-type operators, which interpolate a given function and some of its derivatives on the border of a triangle with one curved side, as well as some of their product and Boolean sum operators. We study the interpolation properties and the order of accuracy (degree of exactness and precision set) of the constructed operators, respectively the remainders of the corresponding interpolation formulas. Finally, we give some numerical examples.
ISSN:	0006-3835 1572-9125
DOI:	10.1007/s10543-010-0256-6