Locally equilibrated stress recovery for goal oriented error estimation in the extended finite element method

TL;DR

This paper introduces a locally equilibrated stress recovery method for goal-oriented error estimation in extended finite element methods, enhancing accuracy in complex domain simulations by focusing on stress intensity factors.

Contribution

It proposes a novel equilibrated recovery technique tailored for enriched finite element approximations, specifically targeting stress intensity factors as the key quantity of interest.

Findings

Improved stress field accuracy through local equilibrated recovery.

Enhanced error estimation for complex domain simulations.

Effective application to extended finite element methods.

Abstract

Goal oriented error estimation and adaptive procedures are essential for the accurate and efficient evaluation of numerical simulations that involve complex domains. By locally improving the approximation quality we can solve expensive problems which could result intractable otherwise. Here, we present an error estimation technique for enriched finite element approximations that is based on an equilibrated recovery technique, which considers the stress intensity factor as the quantity of interest. The locally equilibrated superconvergent patch recovery is used to obtain enhanced stress fields for the primal and dual problems defined to evaluate the error estimate.