hp-discontinuous Galerkin time stepping for parabolic problems

The algorithmic pattern of the lip-discontinuous Galerkin finite element me thod (DGFEM) for the time semidiscretization of parabolic evolution equatio ns is presented. In combination with a continuous hp-discretization in spac e we obtain a fully discrete hp-scheme for the numerical solution of parabo lic problems. Numerical examples for the heat equation in a two-dimensional domain confirm the exponential convergence rates which are predicted by th eoretical results, under realistic assumptions on the initial data and the forcing terms. We also compare different methods to reduce the computationa l cost of the DGFEM. (C) 2001 Elsevier Science B.V. All rights reserved.