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Higher‐order natural element methods: Towards an isogeometric meshless method

The problem of generalizing the natural element method (NEM) in terms of higher‐order consistency and continuity is addressed here. It is done by means of the de Boor algorithm, the same employed to obtain B‐splines by linear combinations of linear interpolants in one dimension. By noting that any form of natural neighbour interpolation can be considered as a suitable generalization of linear interpolation to two and higher dimensions, the de Boor algorithm is extended to two or higher dimensions, thus obtaining a new form of interpolation that can be used in a Galerkin framework to develop a new class of meshless methods.