A novel approach to implicit residual-type error estimation in mesh-free methods and an adaptive refinement strategy are presented. This allows computing upper and lower bounds of the error in energy norm with the ultimate goal of obtaining bounds for outputs of interest. The proposed approach precludes the main drawbacks of standard residual-type estimators circumventing the need of flux-equilibration and resulting in a simple implementation that avoids integrals on edges/sides of a domain decomposition (mesh). This is especially interesting for mesh-free methods. The adaptive strategy proposed leads to a fast convergence of the bounds to the desired precision.

This is the pre-peer reviewed version of the following article: Vidal, Y. [et al.]. Bounds for quantities of interest and adaptivity in the element-free Galerkin method. "International journal for numerical methods in engineering", Juliol 2008, vol. 76, núm. 11, p. 1782-1818., which has been published in final form at http://www3.interscience.wiley.com/journal/120749792/abstract