An h-adaptive element-free Galerkin meshless method using a posteriori error estimator

This paper provides an automatic h-refinement procedure for the element-free Galerkin (EFG) meshless method. This technique uses a posteriori Zienkiewicz and Zhu (Z-Z) error estimator based on super-convergent patch recovery where Gauss points are supposed to be super-convergent. The obtained recovered stresses are smooth and free of spurious oscillations observed in the EFG method. The error is calculated using the difference between the numerical and smoothed stresses, and the re-meshing is applied to the Gauss cells where the calculated error exceeds the admissible imposed error. Several examples are presented for linear and elastic problems showing the effectivity of the proposed approach.