A local discontinuous Galerkin method for time-fractional diffusion equation with discontinuous coefficient

Abstract In this paper, a fully discrete Local discontinuous Galerkin (LDG) method is discussed for a time-fractional reaction diffusion initial-boundary value problem with discontinuous diffusive coefficient. In this method the well-known L2- 1 σ scheme on graded meshes is presented to deal with the weak singularity at initial time t = 0 , while in the spatial direction a LDG method on a uniform mesh is presented to handle the discontinuous coefficient. By the discrete fractional Gronwall inequality, the L 2 -norm stability and consistency estimate results are derived for the proposed fully discrete LDG method. Numerical experiments are presented to verify the sharpness of the error analysis.