Lagrangian and moving mesh methods for the convection diffusion equation

摘要

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.