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

Gonzalez Estrada, Octavio Andres, Nadal, E., Ródenas, J. J., Kerfriden, Pierre ORCID:, Bordas, Stephane Pierre Alain ORCID: and Fuenmayor, F. J. 2014. Mesh adaptivity driven by goal-oriented locally equilibrated superconvergent patch recovery. Computational Mechanics 53 (5) , pp. 957-976. 10.1007/s00466-013-0942-8

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Goal-oriented error estimates (GOEE) have become popular tools to quantify and control the local error in quantities of interest (QoI), which are often more pertinent than local errors in energy for design purposes (e.g. the mean stress or mean displacement in a particular area, the stress intensity factor for fracture problems). These GOEE are one of the key unsolved problems of advanced engineering applications in, for example, the aerospace industry. This work presents a simple recovery-based error estimation technique for QoIs whose main characteristic is the use of an enhanced version of the Superconvergent Patch Recovery (SPR) technique previously used for error estimation in the energy norm. This enhanced SPR technique is used to recover both the primal and dual solutions. It provides a nearly statically admissible stress field that results in accurate estimations of the local contributions to the discretisation error in the QoI and, therefore, in an accurate estimation of this magnitude. This approach leads to a technique with a reasonable computational cost that could easily be implemented into already available finite element codes, or as an independent postprocessing tool.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Advanced Research Computing @ Cardiff (ARCCA)
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Uncontrolled Keywords: Goal-oriented; Error estimation; Recovery; Quantities of interest; Error control; Mesh adaptivity
Publisher: Springer
ISSN: 0178-7675
Funders: EU FP7, EPSRC, European Research Council (ERC), Ministerio de Economía y Competitividad (Spain), FPU, Universitat Politècnica de València, Generalitat Valenciana
Last Modified: 11 Mar 2023 02:13

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