Mesh Refinement For Stabilized Convection Diffusion Equations

B. Achchab; M. El Fatini; A. Souissi

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 7, page 73-77
  • ISSN: 0973-5348

Abstract

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

How to cite

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Achchab, B., El Fatini, M., and Souissi, A.. Taik, A., ed. "Mesh Refinement For Stabilized Convection Diffusion Equations." Mathematical Modelling of Natural Phenomena 5.7 (2010): 73-77. <http://eudml.org/doc/197657>.

@article{Achchab2010,
abstract = {We derive a residual a posteriori error estimates for the subscales stabilization of convection diffusion equation. The estimator yields upper bound on the error which is global and lower bound that is local},
author = {Achchab, B., El Fatini, M., Souissi, A.},
editor = {Taik, A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {a posteriori error estimates; convection diffusion equation; stabilization},
language = {eng},
month = {8},
number = {7},
pages = {73-77},
publisher = {EDP Sciences},
title = {Mesh Refinement For Stabilized Convection Diffusion Equations},
url = {http://eudml.org/doc/197657},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Achchab, B.
AU - El Fatini, M.
AU - Souissi, A.
AU - Taik, A.
TI - Mesh Refinement For Stabilized Convection Diffusion Equations
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/8//
PB - EDP Sciences
VL - 5
IS - 7
SP - 73
EP - 77
AB - We derive a residual a posteriori error estimates for the subscales stabilization of convection diffusion equation. The estimator yields upper bound on the error which is global and lower bound that is local
LA - eng
KW - a posteriori error estimates; convection diffusion equation; stabilization
UR - http://eudml.org/doc/197657
ER -

References

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  1. B. Achchab, M. El Fatini, A. Ern, A. Souissi. Adaptive mesh for algebraic orthogonal subscale stabilization of convective dispersive transport. C. R. Math. Acad. Sci. Paris., 346 (2008), 1187–1190. Zbl1154.65080
  2. B. Achchab, M. El Fatini, A. Ern, A. Souissi. A posteriori error estimator for subgrid viscosity stabilisation applied to convection-diffusion problem. AML, 22 (2009), No. 9, 1418–1424. Zbl1173.65350
  3. F. Brezzi, A. Russo. Chosing bubbles for advection-diffusion problems. Math. Model. and Meth. Appl. Sci., 4 (1994), 571–587. Zbl0819.65128
  4. A. N. Brooks, T. J. R. Hughes. 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. Zbl0497.76041
  5. R. Codina. On stabilized finite element methods for linear systems of convection-diffusion-reaction equations. Comp. Meth. Appl. Mech. Engrg., 188 (2000), 61–82. Zbl0973.76041
  6. J. L. Guermond. Subgrid Stabilization of Galerkin approximations of linear monotone operators. Journal of Numerical Analysis (IMA), 21 (2001), 165–197. Zbl0974.65059
  7. T. J. R. Hughes. 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. Zbl0866.76044
  8. O. Pironneau. On the transport-diffusion algorithm and its applications to the Navier-Stokes equations. Numer. Math., 38 (1982), 309–332. Zbl0505.76100
  9. R. Verfürth. A posteriori error estimators for convection-diffusion equations. Numer. Math., 80 (1998), 641–663. Zbl0913.65095

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