Central local discontinuous Galerkin method for the space fractional diffusion equation
It offers a new numerical method for solving space fractional diffusion equations, which are important in modeling anomalous diffusion, but the contribution is incremental as it extends existing LDG techniques.
The paper develops a central local discontinuous Galerkin method for space fractional diffusion equations, providing stability analysis and error estimates, and validates the scheme with 1D and 2D numerical experiments.
This paper provides the semi-discrete scheme by the central local discontinuous Galerkin method for space fractional diffusion equation on two sets of overlapping cells, and then we give the stability analysis and error estimates for the scheme. Lastly, we verify the effectiveness of the proposed scheme by the one- and two-dimensional numerical experiments.