Geodesic
Lagrangian and moving mesh methods for the convection diffusion equation
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 42 (2008) no. 1, pp. 25-55

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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.

DOI : 10.1051/m2an:2007053
Classification : 65M60, 65M15
Keywords: convection diffusion, moving meshes, lagrangian formulation 
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     author = {Chrysafinos, Konstantinos and Walkington, Noel J.},
     title = {Lagrangian and moving mesh methods for the convection diffusion equation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {25--55},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {1},
     year = {2008},
     doi = {10.1051/m2an:2007053},
     mrnumber = {2387421},
     zbl = {1136.65089},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007053/}
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Chrysafinos, Konstantinos; Walkington, Noel J. Lagrangian and moving mesh methods for the convection diffusion equation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 42 (2008) no. 1, pp. 25-55. doi: 10.1051/m2an:2007053

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