# A Posteriori Error Estimates on Stars for Convection Diffusion Problem

B. Achchab; A. Agouzal; K. Bouihat

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 5, Issue: 7, page 67-72
- ISSN: 0973-5348

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topAchchab, B., Agouzal, A., and Bouihat, K.. Taik, A., ed. "A Posteriori Error Estimates on Stars for Convection Diffusion Problem." Mathematical Modelling of Natural Phenomena 5.7 (2010): 67-72. <http://eudml.org/doc/197720>.

@article{Achchab2010,

abstract = {In this paper, a new a posteriori error estimator for nonconforming convection diffusion
approximation problem, which relies on the small discrete problems solution in stars, has
been established. It is equivalent to the energy error up to data oscillation without any
saturation assumption nor comparison with residual estimator},

author = {Achchab, B., Agouzal, A., Bouihat, K.},

editor = {Taik, A.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {a posteriori error estimator; nonconforming finite elements method; convection diffusion equations},

language = {eng},

month = {8},

number = {7},

pages = {67-72},

publisher = {EDP Sciences},

title = {A Posteriori Error Estimates on Stars for Convection Diffusion Problem},

url = {http://eudml.org/doc/197720},

volume = {5},

year = {2010},

}

TY - JOUR

AU - Achchab, B.

AU - Agouzal, A.

AU - Bouihat, K.

AU - Taik, A.

TI - A Posteriori Error Estimates on Stars for Convection Diffusion Problem

JO - Mathematical Modelling of Natural Phenomena

DA - 2010/8//

PB - EDP Sciences

VL - 5

IS - 7

SP - 67

EP - 72

AB - In this paper, a new a posteriori error estimator for nonconforming convection diffusion
approximation problem, which relies on the small discrete problems solution in stars, has
been established. It is equivalent to the energy error up to data oscillation without any
saturation assumption nor comparison with residual estimator

LA - eng

KW - a posteriori error estimator; nonconforming finite elements method; convection diffusion equations

UR - http://eudml.org/doc/197720

ER -

## References

top- 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. Zbl1254.65122
- A. Agouzal. A posteriori error estimator for nonconforming finite element methods. Appl. Math. Lett., 7 (1994), No. 5, 61-66. Zbl0810.65096
- M. Ainsworth, I. Babuska. Reliable and robust a posteriori error estimating for singularly perturbed reaction-diffusion problems. SIAM J. Numer. Anal., 36 (1999), 331-353. Zbl0948.65114
- R.E. Bank, A. Weiser. Some a posteriori error estimators for elliptic partial differential equations. Math. Comp., 44 (1985), 283-301. Zbl0569.65079
- E. Dari, R. Durán, C. Padra. Error estimators for nonconforming finite element approximations of the Stokes problem . Math. Comput., 64 (1995), No. 211, 1017-1033. Zbl0827.76042
- P. Morin, R.H. Nochetto, K.G. Siebert. Local problems on stars: a posteriori error estimators, convergence and performance. Math. Comp., 72 (2003), 1067-1097. Zbl1019.65083
- R.H. Nochetto. Removing the saturation assumption in a posteriori error analysis. Istit. Lombardo. Sci. Lett. Rend. A., 127 (1993), 67-82. Zbl0878.65088
- R. Verfürth. Robust a posteriori error estimates for stationary convection-diffusion equations. SIAM J. Numer. Anal., 43 (2005), 1766-1782. Zbl1099.65100

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