  We present a novel structure-preserving numerical scheme for discontinuous
finite element approximations of nonlinear hyperbolic systems. The method can
be understood as a generalization of the Lax-Friedrichs flux to a high-order
staggered grid and does not depend on any tunable parameters. Under a presented
set of conditions, we show that the method is conservative and invariant domain
preserving. Numerical experiments on the Euler equations show the ability of
the scheme to resolve discontinuities without introducing excessive spurious
oscillations or dissipation.
