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Mathematical Problems in Engineering
Volume 2014, Article ID 518727, 11 pages
Research Article

The Interpolating Boundary Element-Free Method for Unilateral Problems Arising in Variational Inequalities

College of Mathematics Science, Chongqing Normal University, Chongqing 400047, China

Received 26 November 2013; Revised 30 December 2013; Accepted 31 December 2013; Published 12 February 2014

Academic Editor: Yumin Cheng

Copyright © 2014 Fen Li and Xiaolin Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The interpolating boundary element-free method (IBEFM) is developed in this paper for boundary-only analysis of unilateral problems which appear in variational inequalities. The IBEFM is a direct boundary only meshless method that combines an improved interpolating moving least-square scheme for constructing interpolation functions with boundary integral equations (BIEs) for representing governing equations. A projection operator is used to formulate the BIEs and then the formulae of the IBEFM are obtained for unilateral problems. The convergence of the developed meshless method is derived mathematically. The capability of the method is also illustrated and assessed through some numerical experiments.