scholarly journals High Order Maximum-Principle-Preserving Discontinuous Galerkin Method for Convection-Diffusion Equations

2015 ◽  
Vol 37 (2) ◽  
pp. A583-A608 ◽  
Author(s):  
Tao Xiong ◽  
Jing-Mei Qiu ◽  
Zhengfu Xu
Keyword(s):  
Maximum Principle ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
High Order ◽  
Diffusion Equations ◽  
Convection Diffusion

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.

Sign in / Sign up

Export Citation Format

Share Document