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Error analysis of the reproducing kernel particle method

✍ Scribed by Weimin Han; Xueping Meng

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 603 KB
Volume: 190
Category: Article
ISSN: 0045-7825
DOI: 10.1016/s0045-7825(01)00214-6

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✦ Synopsis

Interest in meshfree (or meshless) methods has grown rapidly in recent years in solving boundary value problems (BVPs) arising in mechanics, especially in dealing with dicult problems involving large deformation, moving discontinuities, etc. In this paper, we provide a theoretical analysis of the reproducing kernel particle method (RKPM), which belongs to the family of meshfree methods. One goal of the paper is to set up a framework for error estimates 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 estimates can be used to yield error estimates for RKP solutions of BVPs.

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