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.

The topic of this work is to obtain discrete Sobolev inequalities for piecewise constant functions, and to deduce L p error estimates on the approximate solutions of convection diffusion equations by finite volume schemes.

Classification : 65N15
Mots clés : finite volume methods, ${L^p}$ error estimates, unstructured meshes, convection-diffusion equations
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     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},
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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://www.numdam.org/item/M2AN_2001__35_4_767_0/

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