An Adaptive Multi-level method for Convection Diffusion Problems

Martine Marion; Adeline Mollard

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 34, Issue: 2, page 439-458
  • ISSN: 0764-583X

Abstract

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In this article we introduce an adaptive multi-level method in space and time for convection diffusion problems. The scheme is based on a multi-level spatial splitting and the use of different time-steps. The temporal discretization relies on the characteristics method. We derive an a posteriori error estimate and design a corresponding adaptive algorithm. The efficiency of the multi-level method is illustrated by numerical experiments, in particular for a convection-dominated problem.

How to cite

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Marion, Martine, and Mollard, Adeline. " An Adaptive Multi-level method for Convection Diffusion Problems." ESAIM: Mathematical Modelling and Numerical Analysis 34.2 (2010): 439-458. <http://eudml.org/doc/197405>.

@article{Marion2010,
abstract = { In this article we introduce an adaptive multi-level method in space and time for convection diffusion problems. The scheme is based on a multi-level spatial splitting and the use of different time-steps. The temporal discretization relies on the characteristics method. We derive an a posteriori error estimate and design a corresponding adaptive algorithm. The efficiency of the multi-level method is illustrated by numerical experiments, in particular for a convection-dominated problem. },
author = {Marion, Martine, Mollard, Adeline},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Multi-level methods; convection-diffusion equations; characteristics method; a posteriori error estimates; adaptive algorithms.; adaptive multi-level method; convection diffusion problems; characteristics method; error estimate; numerical experiments},
language = {eng},
month = {3},
number = {2},
pages = {439-458},
publisher = {EDP Sciences},
title = { An Adaptive Multi-level method for Convection Diffusion Problems},
url = {http://eudml.org/doc/197405},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Marion, Martine
AU - Mollard, Adeline
TI - An Adaptive Multi-level method for Convection Diffusion Problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 2
SP - 439
EP - 458
AB - In this article we introduce an adaptive multi-level method in space and time for convection diffusion problems. The scheme is based on a multi-level spatial splitting and the use of different time-steps. The temporal discretization relies on the characteristics method. We derive an a posteriori error estimate and design a corresponding adaptive algorithm. The efficiency of the multi-level method is illustrated by numerical experiments, in particular for a convection-dominated problem.
LA - eng
KW - Multi-level methods; convection-diffusion equations; characteristics method; a posteriori error estimates; adaptive algorithms.; adaptive multi-level method; convection diffusion problems; characteristics method; error estimate; numerical experiments
UR - http://eudml.org/doc/197405
ER -

References

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  4. J.B. Burie and M. Marion, Adaptative multi-level methods in space and time for paraboloc problems- The periodic case. Math. of Comp. (to appear).  
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  12. M. Marion and A. Mollard, A multi-level characteristics method for periodic convection-dominated diffusion problems. Numer. Meth. PDEs. (to appear).  
  13. M. Marion and J. Xu, Error estimates on a new nonlinear Galerkin method based on two-grid finite elements. SIAM J. Numer. Anal.32 (1995) 1170-1184.  
  14. A. Mollard, Méthodes de caractéristiques multi-niveaux en espace et en temps pour une équation de convection-diffusion - Cas d'une approximation pseudo-spectrale, Thèse, École Centrale de Lyon (1998).  
  15. O. Pironneau, Finite element methods for fluids, Masson (1989).  
  16. E. Suli, Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes Equations. Numer. Math.53 (1988) 459-483.  
  17. E. Suli and A.F. Ware, A spectral method of characteristics for hyperbolic problems. SIAM. J. Numer. Anal.28 (1991) 423-445.  

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