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.
Mots-clés : finite volume methods, ${L^p}$ error estimates, unstructured meshes, convection-diffusion equations
@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: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {767--778},
publisher = {EDP-Sciences},
volume = {35},
number = {4},
year = {2001},
mrnumber = {1863279},
zbl = {0990.65122},
language = {en},
url = {http://archive.numdam.org/item/M2AN_2001__35_4_767_0/}
}
TY - JOUR AU - Coudière, Yves AU - Gallouët, Thierry AU - Herbin, Raphaèle TI - Discrete Sobolev inequalities and $L^p$ error estimates for finite volume solutions of convection diffusion equations JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2001 SP - 767 EP - 778 VL - 35 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/item/M2AN_2001__35_4_767_0/ LA - en ID - M2AN_2001__35_4_767_0 ER -
%0 Journal Article %A Coudière, Yves %A Gallouët, Thierry %A Herbin, Raphaèle %T Discrete Sobolev inequalities and $L^p$ error estimates for finite volume solutions of convection diffusion equations %J ESAIM: Modélisation mathématique et analyse numérique %D 2001 %P 767-778 %V 35 %N 4 %I EDP-Sciences %U http://archive.numdam.org/item/M2AN_2001__35_4_767_0/ %G en %F 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: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 4, pp. 767-778. http://archive.numdam.org/item/M2AN_2001__35_4_767_0/
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