High-Order Discontinuous Galerkin Time Stepping

The focus of this talk is to provide an analytical framework for arbitrary-order (hp-type) discontinuous Galerkin (dG) time discretizations.For this purpose, we will introduce and analyze a discrete dG time derivative operator within a general Hilbert space setting; this will turn out to be a crucial tool in the numerical analysis of the dG method. Specifically, we will illustrate the general functionality of the dG operator in the context of existence proofs of discrete dG solutions for general nonlinear initial value problems (including blow-up problems) as well as in the derivation of a posteriori error estimates for linear parabolic problems.