Open Access

ARTICLE

On a Meshfree Method for Singular Problems

Weimin Han, Xueping Meng¹

1 Department of Mathematics, University of Iowa, Iowa City, IA 52242, U.S.A.

Computer Modeling in Engineering & Sciences 2002, 3(1), 65-76. https://doi.org/10.3970/cmes.2002.003.065

Abstract

Interests in meshfree (or meshless) methods have grown rapidly in the recent years in solving boundary value problems arising in mechanics, especially in dealing with difficult problems involving large deformation, moving discontinuities, etc. Rigorous error estimates of a meshfree method, the reproducing kernel particle method, for smooth solutions have been theoretically derived and experimentally tested in Han, Meng (2001). In this paper, we provide an error analysis of the meshfree method for solving problems with singular solutions. The results are presented in the context of one-dimensional problems. The error estimates are of optimal order and are supported by numerical results.

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