Element Free Galerkin Post-processing Technique Based Error Estimator for Elasticity Problems

The study present a Mesh Free based post-processing technique for asymptotically (upper) bounded error estimator for Finite Element Analyses of elastic problems. The proposed technique uses Galerkin Element Free procedure for recovery of the displacement derivatives over a patch of nodes in radial domains. The radial nodes patches are used to construct the trial shape functions utilizing the moving least-squares (MLS) techniques. The proposed technique has been tested on three benchmark elastic problems discretized using ۴-node quadrilateral elements. The recovered nodal stresses are utilized to calculate the error in finite element solution in energy norm. The study also demonstrates adaptive analysis application of proposed error estimator. The performance of proposed error estimator based on mesh independent node patches has been compared with that of mesh dependent node patches based Zienkiewicz-Zhu (ZZ) error estimator on structured and unstructured mesh. The improved results of the proposed error estimator in terms of convergence rate and effectivity are obtained. It is shown that present study incorporates the superiority of the Mesh Free Galerkin method into finite element analysis environment.