Lagrangian and moving mesh methods for the convection diffusion equation

Konstantinos Chrysafinos; Noel J. Walkington

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

  • Volume: 42, Issue: 1, page 25-55
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Chrysafinos, Konstantinos, and Walkington, Noel J.. "Lagrangian and moving mesh methods for the convection diffusion equation." ESAIM: Mathematical Modelling and Numerical Analysis 42.1 (2008): 25-55. <http://eudml.org/doc/250339>.

@article{Chrysafinos2008,
abstract = { 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. },
author = {Chrysafinos, Konstantinos, Walkington, Noel J.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Convection diffusion; moving meshes; Lagrangian formulation.; Lagrangian formulation; convection-diffusion equation; error estimates; finite element; convection dominated flows},
language = {eng},
month = {1},
number = {1},
pages = {25-55},
publisher = {EDP Sciences},
title = {Lagrangian and moving mesh methods for the convection diffusion equation},
url = {http://eudml.org/doc/250339},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Chrysafinos, Konstantinos
AU - Walkington, Noel J.
TI - Lagrangian and moving mesh methods for the convection diffusion equation
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2008/1//
PB - EDP Sciences
VL - 42
IS - 1
SP - 25
EP - 55
AB - 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.
LA - eng
KW - Convection diffusion; moving meshes; Lagrangian formulation.; Lagrangian formulation; convection-diffusion equation; error estimates; finite element; convection dominated flows
UR - http://eudml.org/doc/250339
ER -

References

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Citations in EuDML Documents

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  1. Konstantinos Chrysafinos, Sotirios P. Filopoulos, Theodosios K. Papathanasiou, Error estimates for a FitzHugh–Nagumo parameter-dependent reaction-diffusion system
  2. Konstantinos Chrysafinos, Sotirios P. Filopoulos, Theodosios K. Papathanasiou, Error estimates for a FitzHugh–Nagumo parameter-dependent reaction-diffusion system
  3. Konstantinos Chrysafinos, Convergence of discontinuous Galerkin approximations of an optimal control problem associated to semilinear parabolic PDE's

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