Meshless cubature over the disk using thin-plate splines

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. (C) 2007 Elsevier B.V. All rights reserved.