The meshless standard and hypersingular boundary node methods-applicationsto error estimation and adaptivity in three-dimensional problems

The standard (singular) boundary node method (BNM) and the novel hypersingu lar boundary node method (HBNM) are employed for the usual and adaptive sol utions of three-dimensional potential and elasticity problems. These method s couple boundary integral equations with moving least-squares interpolants while retaining the dimensionality advantage of the former and the meshles s attribute of the latter. The 'hypersingular residuals', developed for err or estimation in the mesh-based collocation boundary element method (BEM) a nd symmetric Galerkin BEM by Paulino et al., are extended to the meshless B NM setting. A simple 'a posteriori' error estimation and an effective adapt ive refinement procedure are presented. The implementation of all the techn iques involved in this work are discussed, which includes aspects regarding parallel implementation of the BNM and HBNM codes. Several numerical examp les are given and discussed in detail. Conclusions are inferred and relevan t extensions of the methodology introduced in this work are provided. Copyr ight (C) 2001 John Wiley & Sons, Ltd.