Introduction

Natural neighbor (n-n) interpolation [1,2,3] is a multivariate data interpolation method, which has primarily been used in data interpolation and modeling of geophysical phenomena. See [4] for a review on scattered data interpolation in multi-dimensions. Natural neighbor interpolation relies on concepts, such as Voronoi diagrams [5] and Delaunay tessellations [6] in computational geometry [7,8], in order to construct the interpolant. It is a weighted average method, where the weights are area-based, as opposed to Shepard's interpolant (to cite an example), where distance-based weights are used. In spite of its fairly simple structure, sound theoretical basis for construction, and desirable smoothness properties, n-n interpolation has seemingly received little attention in the area of multivariate data interpolation, when compared to other interpolation/approximation schemes such as Shepard's interpolant, moving least squares approximants, radial basis functions, or Hardy's multiquadrics. Recent work on n-n interpolation [9] and its application to the solution of partial differential equations [10] does exemplify the potential of the Natural Element Method (NEM), and hence begs the question if it could find possible applications in the field of computational solid/fluid mechanics. This note, in the same spirit, attempts to give a brief introduction to the interpolation scheme and its implementation in a Galerkin-based formulation (NEM) to solve partial differential equations. The interested reader can refer to the references (and the references therein) for further details.