Superconvergence of a discontinuous Galerkin method for fractional diffusion and wave equations

Kassem Mustapha, William McLean

We consider an initial-boundary value problem for ${\partial }_{t}u-{\partial }_t^{-\alpha }{\nabla }^{2}u=f(t)$, that is, for a fractional diffusion ($-1<\alpha <0$) or wave ($0<\alpha <1$) equation. A numerica…