In this article, we present a numerical scheme based on a finite element method in order to solve a time-dependent convection-diffusion equation problem and satisfy some conservation properties. In particular, our scheme is able to conserve the total energy for a heat equation or the total mass of a solute in a fluid for a concentration equation, even if the approximation of the velocity field is not completely divergence-free. We establish a priori errror estimates for this scheme and we give some numerical examples which show the efficiency of the method.
Mots-clés : finite elements, numerical conservation schemes, Robin boundary condition, convection-diffusion equations
@article{M2AN_2013__47_6_1765_0,
author = {Flotron, St\'ephane and Rappaz, Jacques},
title = {Conservation schemes for convection-diffusion equations with {Robin} boundary conditions},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1765--1781},
publisher = {EDP-Sciences},
volume = {47},
number = {6},
year = {2013},
doi = {10.1051/m2an/2013087},
mrnumber = {3123375},
zbl = {1293.65129},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2013087/}
}
TY - JOUR AU - Flotron, Stéphane AU - Rappaz, Jacques TI - Conservation schemes for convection-diffusion equations with Robin boundary conditions JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2013 SP - 1765 EP - 1781 VL - 47 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2013087/ DO - 10.1051/m2an/2013087 LA - en ID - M2AN_2013__47_6_1765_0 ER -
%0 Journal Article %A Flotron, Stéphane %A Rappaz, Jacques %T Conservation schemes for convection-diffusion equations with Robin boundary conditions %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 1765-1781 %V 47 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2013087/ %R 10.1051/m2an/2013087 %G en %F M2AN_2013__47_6_1765_0
Flotron, Stéphane; Rappaz, Jacques. Conservation schemes for convection-diffusion equations with Robin boundary conditions. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 6, pp. 1765-1781. doi : 10.1051/m2an/2013087. http://www.numdam.org/articles/10.1051/m2an/2013087/
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