High-Order Accurate Runge-Kutta (Local) Discontinuous Galerkin Methods for One- and Two-Dimensional Fractional Diffusion Equations

2012 ◽  
Vol 5 (3) ◽  
pp. 333-358 ◽  
Author(s):  
Xia Ji and Huazhong Tang
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Fractional Diffusion ◽  
High Order ◽  
Diffusion Equations ◽  
Galerkin Methods ◽  
Two Dimensional ◽  
Fractional Diffusion Equations ◽  
Local Discontinuous Galerkin ◽  
Local Discontinuous Galerkin Methods

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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