Error analysis of the reproducing kernel particle method

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 difficult problems involving large deformation, moving discontinuities, etc. In this paper, we provide a theoretical analysis of the...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2001-09, Vol.190 (46), p.6157-6181
Main Authors: Han, Weimin, Meng, Xueping
Format: Article
Language:English
Subjects:
Computational methods in continuum mechanics
Continuum mechanics (soil mechanics...)
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Meshfree methods
Meshless methods
Optimal order error estimates
Physics
Regular particle distributions
Reproducing kernel particle method (RKPM)
Solid mechanics
Structural and continuum mechanics
Theory and numerical methods
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Summary: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 difficult 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.
ISSN:0045-7825
1879-2138
DOI:10.1016/S0045-7825(01)00214-6