On error estimation and adaptive refinement for element free Galerkin method. Part II : adaptive refinement

Abstract

In this paper, an adaptive refinement procedure using the element free Galerkin method (EFGM) for the solution of 2D linear elastostatic problems is suggested. Based on the numerical experiments done in Part I of the current study, in the proposed adaptive refinement scheme, the Zienkiewicz and Zhu (Z-Z) error estimator using the TBelytschko (TB) stress recovery scheme is employed for the a posteriori error estimation of EFGM solution. By considering the a priori convergence rate of the EFGM solution and the estimated error norm, an adaptive refinement strategy for the determination of optimal node spacing is proposed. A simple point mesh generation scheme using pre-defined templates to generate new nodes inside the integration cells for adaptive refinement is also developed. The performance of the suggested refinement procedure is tested by using it to solve several benchmark problems. Numerical results obtained indicate that the suggested procedure can lead to the generation of nearly optimal meshes and the effects of singular points inside the problem domain are largely eliminated. The optimal convergence rate of the EFGM analysis is restored and the effectivity indices of the Z-Z error estimator are converging towards the ideal value of unity as the meshes are refined.