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

In this work, a time-fractional reaction diffusion initial-boundary value problem with discontinuous diffusive coefficient is considered. A fully discrete direct discontinuous Galerkin (DDG) method is presented to solve it. In this method, the well-known L1 scheme with graded mesh is presented to deal with the weak singularity at initial time t = 0, while in spatial a DDG method with uniform mesh is presented to handle the discontinuous diffusive coefficient. Then norm stability and consistency estimate results are derived. Numerical experiments are presented to confirm the sharpness of the error analysis.