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

Octavio Andrés González Estrada (1) , Juan José Ródenas García (2) , Stéphane Bordas (3) , E. Nadal (4) , Pierre Kerfriden (3) , F.J. Fuenmayor (4)

1 IMAM - Institute of Mechanics and Advanced Materials
2 DIMM - Departamento de Ingeniería Mecánica y de Materiales
3 School of Engineering [Cardiff]
4 CITV - Centro de Investigación en Tecnología de Vehículos

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.

Mots clés: goal oriented; error estimation; recovery; quantities of interest; error control; mesh adaptivity

Domaines: Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Octavio Andrés González Estrada, Juan José Ródenas García, Stéphane Bordas, E. Nadal, Pierre Kerfriden, et al.. Locally equilibrated stress recovery for goal oriented error estimation in the extended finite element method. 2013. ⟨hal-00850711v2⟩