MESHLESS METHODS - AN OVERVIEW AND RECENT DEVELOPMENTS

Meshless approximations based on moving least-squares, kernels, and pa rtitions of unity are examined. It is shown that the three methods are in most cases identical except for the important fact that partitions of unity enable p-adaptivity to be achieved. Methods for constructing discontinuous approximations and approximations with discontinuous de rivatives are also described. Next, several issues in implementation a re reviewed: discretization (collocation and Galerkin), quadrature in Galerkin and fast ways of constructing consistent moving least-square approximations. The paper concludes with some sample calculations.