scholarly journals The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems

1998 ◽  
Vol 35 (6) ◽  
pp. 2440-2463 ◽  
Author(s):  
Bernardo Cockburn ◽  
Chi-Wang Shu
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Local Discontinuous Galerkin Method ◽  
Time Dependent ◽  
Convection Diffusion ◽  
Local Discontinuous Galerkin ◽  
Diffusion Systems

Local Discontinuous Galerkin Method for Time-Dependent Singularly Perturbed Semilinear Reaction-Diffusion Problems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Yao Cheng ◽  
Chuanjing Song ◽  
Yanjie Mei
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Domain Boundary ◽  
Local Discontinuous Galerkin Method ◽  
Singularly Perturbed ◽  
Time Dependent ◽  
Element Space ◽  
Local Discontinuous Galerkin ◽  
Ldg Method

AbstractLocal discontinuous Galerkin method is considered for time-dependent singularly perturbed semilinear problems with boundary layer. The method is equipped with a general numerical flux including two kinds of independent parameters. By virtue of the weighted estimates and suitably designed global projections, we establish optimal {(k+1)}-th error estimate in a local region at a distance of {\mathcal{O}(h\log(\frac{1}{h}))} from domain boundary. Here k is the degree of piecewise polynomials in the discontinuous finite element space and h is the maximum mesh size. Both semi-discrete LDG method and fully discrete LDG method with a third-order explicit Runge–Kutta time-marching are considered. Numerical experiments support our theoretical results.

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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