Implementation of high-order, discontinuous Galerkin time stepping for fractional diffusion problems

Abstract

The discontinuous Galerkin (dG) method provides a robust and flexible technique for the time integration of fractional diffusion problems. However, a practical implementation uses coefficients defined by integrals that are not easily evaluated. We describe specialised quadrature techniques that efficiently maintain the overall accuracy of the dG method. In addition, we observe in numerical experiments that known superconvergence properties of dG time stepping for classical diffusion problems carry over in a modified form to the fractional-order setting.