The meshless finite element method

Published in Int. Journal for Numerical Methods in Engineering Vol. 58 (6), pp. 893-912, 2003
doi: 10.1002/nme.798

Abstract

A meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n, and the condition that the shape functions depend only on the node positions. Furthermore, the method proposed also shares several of the advantages of the finite element method such as: (a) the simplicity of the shape functions in a large part of the domain; (b) $C^{0}$ continuity between elements, which allows the treatment of material discontinuities, and (c) ease of introduction of the boundary conditions.