Meshless cubature over the disk using thin-plate splines

Authors:
Alessandro Punzi;Alvise Sommariva;Marco Vianello
Affiliations:
Department of Pure and Applied Mathematics, University of Padua, Italy;Department of Pure and Applied Mathematics, University of Padua, Italy;Department of Pure and Applied Mathematics, University of Padua, Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

In some recent papers, the construction of meshless interpolatory cubature formulas using radial basis functions has been studied. In particular, thin-plate splines allow us to conveniently use Green's formula and give good results on scattered samples of small/moderate size over polygons. Here, we discuss the extension to meshless cubature over the disk and its practical implementation.