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 L 2 norm stability and consistency estimate results are derived. Numerical experiments are presented to confirm the sharpness of the error analysis. [ABSTRACT FROM AUTHOR]