Discrete Sobolev inequalities and $L^p$ error estimates for finite volume solutions of convection diffusion equations

Coudière, Yves; Gallouët, Thierry; Herbin, Raphaèle

Geodesic

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Discrete Sobolev inequalities and

L^{p}

error estimates for finite volume solutions of convection diffusion equations

Coudière, Yves ; Gallouët, Thierry ; Herbin, Raphaèle

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 4, pp. 767-778

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Résumé

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.

MR Zbl

Classification : 65N15
Keywords: 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: Mathematical Modelling and Numerical Analysis },
     pages = {767--778},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {4},
     year = {2001},
     mrnumber = {1863279},
     zbl = {0990.65122},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/M2AN_2001__35_4_767_0/}
}

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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: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 4, pp. 767-778. http://geodesic.mathdoc.fr/item/M2AN_2001__35_4_767_0/