Convergence analysis of a LDG method for tempered fractional convection–diffusion equations

Ahmadinia, Mahdi; Safari, Zeinab

doi:10.1051/m2an/2019052

Ahmadinia, Mahdi ; Safari, Zeinab

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 1, pp. 59-78.

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

Résumé

This paper proposes a local discontinuous Galerkin method for tempered fractional convection–diffusion equations. The tempered fractional convection–diffusion is converted to a system of the first order of differential/integral equation, then, the local discontinuous Galerkin method is employed to solve the system. The stability and order of convergence of the method are proven. The order of convergence O(h$$) depends on the choice of numerical fluxes. The provided numerical examples confirm the analysis of the numerical scheme.

DOI : 10.1051/m2an/2019052

Classification : 35R11, 65M60, 65M12
Mots-clés : Local discontinuous method, tempered fractional derivative, stability, error estimates

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     title = {Convergence analysis of a {LDG} method for tempered fractional convection{\textendash}diffusion equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {59--78},
     publisher = {EDP-Sciences},
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Ahmadinia, Mahdi; Safari, Zeinab. Convergence analysis of a LDG method for tempered fractional convection–diffusion equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 1, pp. 59-78. doi : 10.1051/m2an/2019052. http://www.numdam.org/articles/10.1051/m2an/2019052/

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