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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 490127, 12 pages
Research Article

A Meshfree Method for Signorini Problems Using Boundary Integral Equations

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

Received 5 November 2013; Accepted 1 January 2014; Published 18 February 2014

Academic Editor: Khai Ching Ng

Copyright © 2014 Yanlin Ren 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.


This paper presents a meshfree method for the numerical solution of Signorini problems. In this method, a projection iterative algorithm is used to convert the boundary inequality constraints into a fixed point equation. Then, the boundary value problem is reformulated as boundary integral equations and the unknown boundary variables are interpolated by the point interpolation scheme. Thus, only a nodal data structure on the boundary of a domain is required, and boundary conditions can be implemented directly and easily. The convergence of this method is verified theoretically. Numerical examples involving groundwater flow and electropainting problems are also provided to illustrate the performance and usefulness of the method.