Accurate recovery-based upper error bounds for the extended finite element framework

Author (s): Ródenas, J.J.; González-Estrada, O.A.; Díez, P. and Fuenmayor, F.J.
Journal: Computer Methods in Applied Mechanics and Engineering

Volume: 199
Pages: 2607 – 2621
Date: 2010

Abstract:
This paper introduces a recovery-type error estimator yielding upper bounds of the error in energy norm for linear elastic fracture mechanics problems solved using the extended finite element method (XFEM). The paper can be considered as an extension and enhancement of a previous work in which the upper bounds of the error were developed in a FEM framework. The upper bound property requires the recovered solution to be equilibrated and continuous. The proposed technique consists of using a recovery technique, especially adapted to the XFEM framework that yields equilibrium at a local level (patch by patch). Then a postprocess based on the partition of unity concept is used to obtain continuity. The result is a very accurate but only nearly-statically admissible recovered stress field, with small equilibrium defaults introduced by the postprocess. Sharp upper bounds are obtained using a new methodology accounting for the equilibrium defaults, as demonstrated by the numerical tests.

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Bibtex:

@article{Ródenas20102607,
author = "Ródenas, J.J. ; González-Estrada, O.A.; Díez, P. and Fuenmayor, F.J.“,
title = "Accurate recovery-based upper error bounds for the extended finite element framework ",
journal = "Computer Methods in Applied Mechanics and Engineering ",
volume = "199",
number = "37–40",
pages = "2607 - 2621",
year = "2010",
issn = "0045-7825",
doi = "http://dx.doi.org/10.1016/j.cma.2010.04.010",
url = "http://www.sciencedirect.com/science/article/pii/S0045782510001271",
}