Abstract

In this work, an adaptive technique for application of meshless methods in one- and two-dimensional boundary value problems is described. The proposed method is based on the use of implicit functions for the geometry definition, fixed weighted least squares approximation and an error estimation by means of simple formulas and a robust strategy of refinement based on the own nature of the approximation sub-domains utilised. With all these aspects, the proposed method becomes an attractive alternative for the adaptive solutions to partial differential equations in all scopes of engineering. Numerical results obtained from the computational implementation show the efficiency of the present method. © 2009 Elsevier Ltd. All rights reserved.