Mesh adaptivity driven by goal-oriented locally equilibrated superconvergent patch recovery

TL;DR

This paper introduces an advanced goal-oriented error estimation method using an improved Superconvergent Patch Recovery technique to accurately quantify errors in quantities of interest for finite element analysis.

Contribution

It presents a novel recovery-based error estimator leveraging an enhanced SPR method for better accuracy in goal-oriented finite element error estimation.

Findings

Provides accurate error estimates for quantities of interest

Achieves nearly statically admissible stress fields

Improves reliability of adaptive mesh refinement

Abstract

During the last decade there has been an increase on the use of goal-oriented error estimates which help to quantify and control the local error on a quantity of interest (QoI) that might result relevant for design purposes (e.g. the mean stress or mean displacement in a particular area, the stress intensity factor for fracture problems,...). Residual-based error estimators have been used to estimate the error in quantities of interest for finite element approximations. This work presents a recovery-based error estimation technique for QoI whose main characteristic is the use of an enhanced version of the Superconvergent Patch Recovery (SPR) technique developed by Zienkiewicz and Zhu. This enhanced version of the SPR technique, used to recover the primal and dual solutions, provides a nearly statically admissible stress field that results in accurate estimations of the error in the QoI.