hp-Discontinuous Galerkin time stepping for parabolic problems Original Research Article

The algorithmic pattern of the hp-discontinuous Galerkin finite element method (DGFEM) for the time semidiscretization of parabolic evolution equations is presented. In combination with a continuous hp-discretization in space we obtain a fully discrete hp-scheme for the numerical solution of parabolic problems. Numerical examples for the heat equation in a two-dimensional domain confirm the exponential convergence rates which are predicted by theoretical results, under realistic assumptions on the initial data and the forcing terms. We also compare different methods to reduce the computational cost of the DGFEM.