Recovery based error estimation and adaptivity applied to a modified element-free Galerkin method

In this work, we propose an error estimator of the recovery type, which considers the equilibrium and boundary traction conditions, and an h-refinement procedure that is applied to the modified element-free Galerkin (MEFG) method. The approximate solution obtained by the MEFG method satisfies accurately the essential boundary condition. However, the approximate MEFG stress field presents some discontinuities on a neighborhood of the essential boundary condition and may present some spurious oscillations at regions of high stress gradients or discontinuities. Thus, the h-adaptive scheme is responsible for the reduction not only of the global error but also of the local errors associated with the discontinuities and oscillations of the approximate stress field. In order to validate the proposed procedures, we present some numerical solution for some simple problems and consider the analysis of a complex component.