Conservation schemes for convection-diffusion equations with Robin boundary conditions
Flotron, Stéphane ; Rappaz, Jacques
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 47 (2013), p. 1765-1781 / Harvested from Numdam
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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.

Publié le : 2013-01-01
DOI : https://doi.org/10.1051/m2an/2013087
Classification:  65M60,  35K20,  80A20 
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     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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {47},
     year = {2013},
     pages = {1765-1781},
     doi = {10.1051/m2an/2013087},
     mrnumber = {3123375},
     zbl = {1293.65129},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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 - Modélisation Mathématique et Analyse Numérique, Tome 47 (2013) pp. 1765-1781. doi : 10.1051/m2an/2013087. http://gdmltest.u-ga.fr/item/M2AN_2013__47_6_1765_0/

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