hp-discontinuous Galerkin time stepping for parabolic problems
Werder T., Gerdes K., Schoetzau D., Schwab C., Computer Methods in Applied Mathematics and Engineering, 190, 49-50, 6685-6708, 2001
The algorithmic pattern of the lip-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 init.