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Equilibrated patch recovery error estimates: simple and accurate upper bounds of the error

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Díez, PedroMés informacióMés informacióMés informació
Ródenas García, Juan José
Zienkiewicz, Olgierd Cecil
Document typeArticle
Defense date2007-03
PublisherWiley and Sons
Rights accessOpen Access
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
Abstract
This paper introduces a new recovery-type error estimator ensuring local equilibrium and yielding a guaranteed upper bound of the error. The upper bound property requires the recovered solution to be both statically equilibrated and continuous. The equilibrium is obtained locally (patch-by-patch) and the continuity is enforced by a postprocessing based on the partition of the unity concept. This postprocess is expected to preserve the features of the locally equilibrated stress field. Nevertheless, the postprocess phase modifies the equilibrium, which is no longer exactly fulfilled. A new methodology is introduced that yields upper bound estimates by taking into account this lack of equilibrium. This requires computing the L2 norm of the error or relating it with the energy norm. The guaranteed upper bounds are obtained by using a pessimistic bound of the error L2 norm, derived from an eigenvalue problem. Nevertheless, these bounds are not sharp. An additional strategy based on a more accurate assessment of the error L2 norm is introduced, providing sharp estimates, which are practical upper bounds as it is demonstrated in the numerical tests.
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This is the pre-peer reviewed version of the following article: Díez, P.; Rodenas, J.J.; Zienkiewicz, O.C. Equilibrated patch recovery error estimates: simple and accurate upper bounds of the error. "International journal for numerical methods in engineering", Març 2007, vol. 69, núm. 10, p. 2075-2098., which has been published in final form at http://www3.interscience.wiley.com/journal/112751914/abstract
CitationDíez, P.; Rodenas, J.J.; Zienkiewicz, O.C. Equilibrated patch recovery error estimates: simple and accurate upper bounds of the error. "International journal for numerical methods in engineering", Març 2007, vol. 69, núm. 10, p. 2075-2098. 
URIhttp://hdl.handle.net/2117/8167
DOI10.1002/nme.1837
ISSN0029-5981
Publisher versionhttp://www3.interscience.wiley.com/cgi-bin/fulltext/112751914/PDFSTART?CRETRY=1&SRETRY=0
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