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.
Keywords: Local discontinuous method, tempered fractional derivative, stability, error estimates
@article{M2AN_2020__54_1_59_0,
author = {Ahmadinia, Mahdi and Safari, Zeinab},
title = {Convergence analysis of a {LDG} method for tempered fractional convection{\textendash}diffusion equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {59--78},
year = {2020},
publisher = {EDP Sciences},
volume = {54},
number = {1},
doi = {10.1051/m2an/2019052},
mrnumber = {4051846},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2019052/}
}
TY - JOUR AU - Ahmadinia, Mahdi AU - Safari, Zeinab TI - Convergence analysis of a LDG method for tempered fractional convection–diffusion equations JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2020 SP - 59 EP - 78 VL - 54 IS - 1 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2019052/ DO - 10.1051/m2an/2019052 LA - en ID - M2AN_2020__54_1_59_0 ER -
%0 Journal Article %A Ahmadinia, Mahdi %A Safari, Zeinab %T Convergence analysis of a LDG method for tempered fractional convection–diffusion equations %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2020 %P 59-78 %V 54 %N 1 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2019052/ %R 10.1051/m2an/2019052 %G en %F M2AN_2020__54_1_59_0
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
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