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

Abstract

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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

How to cite

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Achchab, 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

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  1. 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
  2. A. Agouzal. A posteriori error estimator for nonconforming finite element methods. Appl. Math. Lett., 7 (1994), No. 5, 61-66. Zbl0810.65096
  3. 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
  4. R.E. Bank, A. Weiser. Some a posteriori error estimators for elliptic partial differential equations. Math. Comp., 44 (1985), 283-301. Zbl0569.65079
  5. 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
  6. 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
  7. R.H. Nochetto. Removing the saturation assumption in a posteriori error analysis. Istit. Lombardo. Sci. Lett. Rend. A., 127 (1993), 67-82. Zbl0878.65088
  8. 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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