hp Discontinuous Galerkin Time Stepping for Parabolic Problems
T. Werder, Klaus Gerdes, Dominik Schötzau, C. William Schwab · Repository for Publications and Research Data (ETH Zurich) · 2000
Abstract We consider the hp-version of the discontinuous Galerkin (DG) time-stepping method for linear parabolic problems with non-symmetric elliptic spatial operators. We derive new analyticity estimates for the exact solutions by means of semigroup techniques. These estimates allow us to show that the hp-DG time-stepping method can resolve start-up singularities at exponential rates of convergence.