The topic of this work is to obtain discrete Sobolev inequalities for piecewise constant functions, and to deduce error estimates on the approximate solutions of convection diffusion equations by finite volume schemes.
@article{M2AN_2001__35_4_767_0,
author = {Coudi\`ere, Yves and Gallou\"et, Thierry and Herbin, Rapha\`ele},
title = {Discrete Sobolev inequalities and $L^p$ error estimates for finite volume solutions of convection diffusion equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {35},
year = {2001},
pages = {767-778},
mrnumber = {1863279},
zbl = {0990.65122},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2001__35_4_767_0}
}
Coudière, Yves; Gallouët, Thierry; Herbin, Raphaèle. Discrete Sobolev inequalities and $L^p$ error estimates for finite volume solutions of convection diffusion equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 35 (2001) pp. 767-778. http://gdmltest.u-ga.fr/item/M2AN_2001__35_4_767_0/
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