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

Octavio Andrés González Estrada (1) , E. Nadal (2) , J.J. Ródenas (2) , Pierre Kerfriden (3) , Stéphane Pierre-Alain Bordas (1) , F.J. Fuenmayor (2)

1 IMAM - Institute of Mechanics and Advanced Materials
2 CITV - Centro de Investigación en Tecnología de Vehículos
3 School of Engineering [Cardiff]

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.

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, E. Nadal, J.J. Ródenas, Pierre Kerfriden, Stéphane Pierre-Alain Bordas, et al.. Mesh adaptivity driven by goal-oriented locally equilibrated superconvergent patch recovery. 2013. ⟨hal-00731876v3⟩