hp-discontinuous Galerkin time stepping for parabolic problems

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.

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