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Lagrangian and moving mesh methods for the convection diffusion equation

Published online by Cambridge University Press:  12 January 2008

Konstantinos Chrysafinos  and
Noel J. Walkington
Konstantinos Chrysafinos
Affiliation:
: Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece. [email protected] Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213 USA. [email protected]
Noel J. Walkington
Affiliation:
Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213 USA. [email protected]
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Abstract

We propose and analyze a semi Lagrangian method for the convection-diffusion equation. Error estimates for both semi and fully discrete finite element approximations are obtained for convection dominated flows. The estimates are posed in terms of the projections constructed in [Chrysafinos and Walkington, SIAM J. Numer. Anal. 43 (2006) 2478–2499; Chrysafinos and Walkington, SIAM J. Numer. Anal. 44 (2006) 349–366] and the dependence of various constants upon the diffusion parameter is characterized. Error estimates independent of the diffusion constant are obtained when the velocity field is computed exactly.

Keywords

Convection diffusionmoving meshesLagrangian formulation.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 42 , Issue 1 , January 2008 , pp. 25 - 55
Copyright
© EDP Sciences, SMAI, 2008

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