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

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(sigma) 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. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.