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A Posteriori Error Estimates on Stars for Convection DiffusionProblem

Published online by Cambridge University Press:  26 August 2010

A. Taik ,
B. Achchab ,
A. Agouzal  and
K. Bouihat
B. Achchab*
Affiliation:
LM2CE, ESTB and FSJES, Hassan 1 st University, B.P. 218, Berrechid, Morocco
A. Agouzal
Affiliation:
University Lyon1, Institute Camille Jordan, UMR 5208, 69100 Villeurbanne, France
K. Bouihat
Affiliation:
LM2CE, ESTB and FSJES, Hassan 1 st University, B.P. 218, Berrechid, Morocco
*
*Corresponding author: E-mail:[email protected]
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Abstract

In this paper, a new a posteriori error estimator for nonconforming convection diffusionapproximation problem, which relies on the small discrete problems solution in stars, hasbeen established. It is equivalent to the energy error up to data oscillation without anysaturation assumption nor comparison with residual estimator

Keywords

a posteriori error estimatornonconforming finite elements methodconvection diffusion equations
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 7: JANO9 – The 9thInternational Conference on Numerical Analysis and Optimization , 2010 , pp. 67 - 72
Copyright
© EDP Sciences, 2010

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References

B. Achchab, A. Agouzal, A. El Fatini, A. Souissi. Robust hierarchical a posteriori error estimates for stabilized convection-diffusion problem. Numer. Meth. Part. Diff. Equats., to appear.
Agouzal, A.. A posteriori error estimator for nonconforming finite element methods . Appl. Math. Lett., 7 (1994), No. 5, 61-66.CrossRefGoogle Scholar
Ainsworth, M., Babuska, I.. Reliable and robust a posteriori error estimating for singularly perturbed reaction-diffusion problems . SIAM J. Numer. Anal., 36 (1999), 331-353.CrossRefGoogle Scholar
Bank, R.E., Weiser, A.. Some a posteriori error estimators for elliptic partial differential equations . Math. Comp., 44 (1985), 283-301.CrossRefGoogle Scholar
Dari, E., Durán, R., Padra, C.. Error estimators for nonconforming finite element approximations of the Stokes problem . Math. Comput., 64 (1995), No. 211, 1017-1033.CrossRefGoogle Scholar
Morin, P., Nochetto, R.H., Siebert, K.G.. Local problems on stars: a posteriori error estimators, convergence and performance . Math. Comp., 72 (2003), 1067-1097.CrossRefGoogle Scholar
Nochetto, R.H.. Removing the saturation assumption in a posteriori error analysis . Istit. Lombardo. Sci. Lett. Rend. A., 127 (1993), 67-82.Google Scholar
Verfürth, R.. Robust a posteriori error estimates for stationary convection-diffusion equations . SIAM J. Numer. Anal., 43 (2005), 1766-1782.CrossRefGoogle Scholar