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. FierroPrimo
;A. VeeserUltimo
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.Pubblicazioni consigliate
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