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, Volume 35 (2001) no. 4, p. 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
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {4},
     year = {2001},
     pages = {767-778},
     zbl = {0990.65122},
     mrnumber = {1863279},
     language = {en},
     url = {http://www.numdam.org/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, Volume 35 (2001) no. 4, pp. 767-778. http://www.numdam.org/item/M2AN_2001__35_4_767_0/

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