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Mesh Refinement For Stabilized Convection DiffusionEquations

Published online by Cambridge University Press:  26 August 2010

A. Taik ,
B. Achchab ,
M. El Fatini  and
A. Souissi
B. Achchab*
Affiliation:
Hassan 1 st University, LM2CE, ESTB and FSJES, B.P. 218, Berrechid, Morocco
M. El Fatini
Affiliation:
Hassan 1 st University, LM2CE, ESTB and FSJES, B.P. 218, Berrechid, Morocco Hassan II University -Mohammadia, LAMS, L3A, FSBM, B.P. 7955, Casablanca, Morocco
A. Souissi
Affiliation:
Mohammed V-Agdal University, GAN, LMA, FSR and LERMA, EMI, B.P. 1014, Rabat, Morocco
*
* Corresponding author: E-mail:[email protected]
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Abstract

We derive a residual a posteriori error estimates for the subscales stabilization ofconvection diffusion equation. The estimator yields upper bound on the error which isglobal and lower bound that is local

Keywords

a posteriori error estimatesconvection diffusion equationstabilization
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 7: JANO9 – The 9thInternational Conference on Numerical Analysis and Optimization , 2010 , pp. 73 - 77
Copyright
© EDP Sciences, 2010

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References

Achchab, B., El Fatini, M., Ern, A., Souissi, A.. Adaptive mesh for algebraic orthogonal subscale stabilization of convective dispersive transport . C. R. Math. Acad. Sci. Paris., 346 (2008), 1187–1190.CrossRefGoogle Scholar
Achchab, B., El Fatini, M., Ern, A., Souissi, A.. A posteriori error estimator for subgrid viscosity stabilisation applied to convection-diffusion problem . AML, 22 (2009), No. 9, 1418–1424.Google Scholar
Brezzi, F., Russo, A.. Chosing bubbles for advection-diffusion problems . Math. Model. and Meth. Appl. Sci., 4 (1994), 571–587.CrossRefGoogle Scholar
Brooks, A. N., Hughes, T. J. R.. Streamline Upwind/ Petrov Galerkin formulation for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations . Model. Comput. Methods Appl. Mech. Engrg., 32 (1982), 1–3.Google Scholar
Codina, R.. On stabilized finite element methods for linear systems of convection-diffusion-reaction equations . Comp. Meth. Appl. Mech. Engrg., 188 (2000), 61–82.CrossRefGoogle Scholar
Guermond, J. L.. Subgrid Stabilization of Galerkin approximations of linear monotone operators . Journal of Numerical Analysis (IMA), 21 (2001), 165–197.CrossRefGoogle Scholar
Hughes, T. J. R.. Multiscale phenomena: Green’s functions, the Dirichlet-to-Neumann formulation, subgrid-scale models, bubbles and the origin of stabilized methods . Comp. Meth. Appl. Mech. Engrg., 127 (1995), 387–401.CrossRefGoogle Scholar
Pironneau, O.. On the transport-diffusion algorithm and its applications to the Navier-Stokes equations . Numer. Math., 38 (1982), 309–332.CrossRefGoogle Scholar
Verfürth, R.. A posteriori error estimators for convection-diffusion equations . Numer. Math., 80 (1998), 641–663.Google Scholar