Space-time FEM for elastic wave propagation — no time stepping

I have been experimenting with a simple space-time finite element formulation for 1D elastodynamics, and I thought the example might be interesting for the Numerics category. The problem is an elastic bar immediately after impact with a rigid wall. The impact itself is not modeled; the calculation starts from the post-impact initial state and follows the subsequent stress-wave propagation, reflection and release. Instead of discretizing space first and then integrating the semi-discrete system...