Local Analysis of the Local Discontinuous Galerkin Method with Generalized Alternating Numerical Flux for One-Dimensional Singularly Perturbed Problem

2017 ◽  
Vol 72 (2) ◽  
pp. 792-819 ◽  
Author(s):  
Yao Cheng ◽  
Qiang Zhang
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Local Discontinuous Galerkin Method ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problem ◽  
Local Analysis ◽  
One Dimensional ◽  
Numerical Flux ◽  
Local Discontinuous Galerkin

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.

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