Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-24T04:27:04.223Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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