For the linear finite element approximation to a linear elliptic model problem, we propose to safeguard the Zienkiewicz-Zhu estimator by an additional estimator for the residual of the averaged gradient. We give a brief account of the theoretical results on reliability, (local) efficiency, and asymptotic exactness of the full estimator and illustrate these properties in numerical tests, incorporating singular solutions and anisotropic ellipticity.

A Safeguarded Zienkiewicz-Zhu estimator / F. Fierro, A. Veeser - In: Numerical Mathematics and Advanced Applications / [a cura di] A. Bermudez de Castro, D. Gomez, P. Quintela, P. Salgado. - Berlin : Springer, 2006. - ISBN 978-3-540-34287-8. - pp. 269-276 (( Intervento presentato al 6. convegno ENUMATH European Conference on Numerical Mathematics and Advanced Applications tenutosi a Santiago de Compostela, Spain nel 2005 [10.1007/978-3-540-34288-5_20].

A Safeguarded Zienkiewicz-Zhu estimator

F. Fierro
Primo
;
A. Veeser
Ultimo
2006

Abstract

For the linear finite element approximation to a linear elliptic model problem, we propose to safeguard the Zienkiewicz-Zhu estimator by an additional estimator for the residual of the averaged gradient. We give a brief account of the theoretical results on reliability, (local) efficiency, and asymptotic exactness of the full estimator and illustrate these properties in numerical tests, incorporating singular solutions and anisotropic ellipticity.
A~posteriori error estimates ; gradient recovery ; averaging ; superconvergence ; adaptive finite elements ; ZZ estimator ; reliablity ; (local) efficiency ; asymptotic exactness ; anisotropy
Settore MAT/08 - Analisi Numerica
2006
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/27921
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