  Interior penalty discontinuous Galerkin discretisations (IPDG) and especially
the symmetric variant (SIPG) for time-domain wave propagation problems are
broadly accepted and widely used due to their advantageous properties. Linear
systems with block structure arise by applying space-time discretisations and
reducing the global system to time-slab problems. The design of efficient and
robust iterative solvers for linear systems from interior penalty
discretisations for hyperbolic wave equations is still a challenging task and
relies on understanding the properties of the systems. In this work the
numerical properties such as the condition number and the distribution of
eigenvalues of different representations of the linear systems coming from
space-time discretisations for elastic wave propagation are numerically
studied. These properties for interior penalty discretisations depend on the
penalisation and on the time interval length.
