Lagrangian and moving mesh methods for the convection diffusion equation
: Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece. firstname.lastname@example.org
2 Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213 USA. email@example.com
Revised: 26 June 2006
Revised: 22 January 2007
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.
Mathematics Subject Classification: 65M60 / 65M15
Key words: Convection diffusion / moving meshes / Lagrangian formulation.
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