Analysis of an Implicit Fully Discrete Local Discontinuous Galerkin Method for the Time-Fractional Kdv Equation

2015 ◽  
Vol 7 (4) ◽  
pp. 510-527 ◽  
Author(s):  
Leilei Wei ◽  
Yinnian He ◽  
Xindong Zhang
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Kdv Equation ◽  
Local Discontinuous Galerkin Method ◽  
Galerkin Methods ◽  
Unconditionally Stable ◽  
Numerical Examples ◽  
Fully Discrete ◽  
Local Discontinuous Galerkin ◽  
Local Discontinuous Galerkin Methods

AbstractIn this paper, we consider a fully discrete local discontinuous Galerkin (LDG) finite element method for a time-fractional Korteweg-de Vries (KdV) equation. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. We show that our scheme is unconditionally stable and convergent through analysis. Numerical examples are shown to illustrate the efficiency and accuracy of our scheme.

scholarly journals NUMERICAL ANALYSIS OF AN IMPLICIT FULLY DISCRETE LOCAL DISCONTINUOUS GALERKIN METHOD FOR THE FRACTIONAL ZAKHAROV–KUZNETSOV EQUATION

2012 ◽  
Vol 17 (4) ◽  
pp. 558-570 ◽  
Author(s):  
Zongxiu Ren ◽  
Leilei Wei ◽  
Yinnian He ◽  
Shaoli Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Local Discontinuous Galerkin Method ◽  
Galerkin Methods ◽  
Fully Discrete ◽  
Local Discontinuous Galerkin ◽  
Local Discontinuous Galerkin Methods

In this paper we develop and analyze an implicit fully discrete local discontinuous Galerkin (LDG) finite element method for a time-fractional Zakharov–Kuznetsov equation. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. We show that our scheme is unconditional stable and L 2 error estimate for the linear case with the convergence rate through analysis.

scholarly journals A Computational Study of an Implicit Local Discontinuous Galerkin Method for Time-Fractional Diffusion Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Leilei Wei ◽  
Xindong Zhang
Keyword(s):  
Discontinuous Galerkin ◽  
Computational Study ◽  
Local Discontinuous Galerkin Method ◽  
Fractional Diffusion ◽  
Galerkin Methods ◽  
Fractional Diffusion Equations ◽  
Fully Discrete ◽  
Local Discontinuous Galerkin ◽  
Local Discontinuous Galerkin Methods ◽  
Numerical Fluxes

We propose, analyze, and test a fully discrete local discontinuous Galerkin (LDG) finite element method for a time-fractional diffusion equation. The proposed method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. By choosing the numerical fluxes carefully, we prove that our scheme is unconditionally stable and convergent. Finally, numerical examples are performed to illustrate the effectiveness and the accuracy of the method.

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