Interpolation Type Stress Recovery Technique Based Error Estimator for Elasticity Problems

Abstract

A finite element method coupled with error estimation has gained considerable prominence in industry. However, effective and reliable error control of finite element solution is always a challenging task particularly for incompressible and large deformations problems. Effective interpolation type gradient recovery based error estimation procedure is proposed in the present study. The recovery is based on Moving Least Squares approximation (mesh free approach) of the displacement field or their derivatives by a higher order polynomial over a patch of nodes in a circular boundary. The performance of error estimation scheme in terms of its effectivity and convergence has been compared with that of Zienkiewicz-Zhu (ZZ) super-convergent recovery scheme by applying the scheme to benchmark elastic problems. Error estimators compute the error in energy norm of the recovered solution both at local and global levels. The adaptive meshing based on guidance of the local error predicted by ZZ and proposed interpolation type error estimators, is also used to study the error distribution in the domain. The proposed mesh independent node patch based recovery scheme is found to be better than that for the mesh dependent node patch based ZZ super convergent recovery scheme.

DOI: http://dx.doi.org/10.5755/j01.mech.24.5.19937