Conservation schemes for convection-diffusion equations with Robin boundary conditions
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 6, pp. 1765-1781.

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.

DOI : 10.1051/m2an/2013087
Classification : 65M60, 35K20, 80A20
Mots-clés : finite elements, numerical conservation schemes, Robin boundary condition, convection-diffusion equations 
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     title = {Conservation schemes for convection-diffusion equations with {Robin} boundary conditions},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1765--1781},
     publisher = {EDP-Sciences},
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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://archive.numdam.org/articles/10.1051/m2an/2013087/

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