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 diffusion, moving meshes, lagrangian formulation
@article{M2AN_2008__42_1_25_0,
author = {Chrysafinos, Konstantinos and Walkington, Noel J.},
title = {Lagrangian and moving mesh methods for the convection diffusion equation},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {25--55},
year = {2008},
publisher = {EDP Sciences},
volume = {42},
number = {1},
doi = {10.1051/m2an:2007053},
mrnumber = {2387421},
zbl = {1136.65089},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an:2007053/}
}
TY - JOUR AU - Chrysafinos, Konstantinos AU - Walkington, Noel J. TI - Lagrangian and moving mesh methods for the convection diffusion equation JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2008 SP - 25 EP - 55 VL - 42 IS - 1 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an:2007053/ DO - 10.1051/m2an:2007053 LA - en ID - M2AN_2008__42_1_25_0 ER -
%0 Journal Article %A Chrysafinos, Konstantinos %A Walkington, Noel J. %T Lagrangian and moving mesh methods for the convection diffusion equation %J ESAIM: Modélisation mathématique et analyse numérique %D 2008 %P 25-55 %V 42 %N 1 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an:2007053/ %R 10.1051/m2an:2007053 %G en %F M2AN_2008__42_1_25_0
Chrysafinos, Konstantinos; Walkington, Noel J. Lagrangian and moving mesh methods for the convection diffusion equation. ESAIM: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 1, pp. 25-55. doi: 10.1051/m2an:2007053
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