Error analysis of the reproducing kernel particle method

Interest in meshfree (or meshless) methods has grown rapidly in recent year s in solving boundary value problems (BVPs) arising in mechanics, especiall y in dealing with difficult problems involving large deformation, moving di scontinuities, etc. In this paper,we provide a theoretical analysis of the reproducing kernel particle method (RKPM), which belongs to the family of m eshfree methods. One goal of the paper is to set up a framework for error e stimates of RKPM. We introduce the concept of a regular family of particle distributions and derive optimal order error estimates for RKP interpolants on a regular family of particle distributions. The interpolation error est imates can be used to yield error estimates for RKP solutions of BVPs. (C) 2001 Elsevier Science B.V. All rights reserved.