Central local discontinuous Galerkin method for the space fractional diffusion equation

TL;DR

This paper introduces a central local discontinuous Galerkin method for solving space fractional diffusion equations, providing stability analysis, error estimates, and numerical validation in one- and two-dimensional cases.

Contribution

The paper develops a novel semi-discrete scheme using the central local discontinuous Galerkin method specifically for space fractional diffusion equations, including stability and error analysis.

Findings

Scheme is stable and convergent.

Numerical experiments confirm effectiveness in 1D and 2D.

Provides error estimates and validation results.

Abstract

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.