Superconvergence of the Local Discontinuous Galerkin Method for One Dimensional Nonlinear Convection-Diffusion Equations

2021 ◽  
Vol 87 (1) ◽  
Author(s):  
Xiaobin Liu ◽  
Dazhi Zhang ◽  
Xiong Meng ◽  
Boying Wu
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Local Discontinuous Galerkin Method ◽  
Diffusion Equations ◽  
Nonlinear Convection ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Local Discontinuous Galerkin

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

2020 ◽  
Vol 54 (1) ◽  
pp. 59-78 ◽  
Author(s):  
Mahdi Ahmadinia ◽  
Zeinab Safari
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Order Of Convergence ◽  
Local Discontinuous Galerkin Method ◽  
Diffusion Equations ◽  
Convection Diffusion ◽  
Local Discontinuous Galerkin ◽  
Differential Integral Equation ◽  
The Stability

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(hk+1) depends on the choice of numerical fluxes. The provided numerical examples confirm the analysis of the numerical scheme.

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