Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-06T02:22:52.356Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Get access

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

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

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