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moving meshes

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Lagrangian and moving mesh methods for the convection diffusion equation
Konstantinos Chrysafinos, Noel J. Walkington
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 42 / Issue 1 / January 2008

Published online by Cambridge University Press:

12 January 2008, pp. 25-55

Print publication:

January 2008
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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.