  The Courant-Friedrichs-Lewy (CFL) condition guarantees the stability of the
popular explicit leapfrog method for the wave equation. However, it limits the
choice of the time step size to be bounded by the minimal mesh size in the
spatial finite element mesh. This essentially prohibits any sort of adaptive
mesh refinement that would be required to reveal optimal convergence rates on
domains with re-entrant corners. This paper shows how a simple subspace
projection step inspired by numerical homogenisation can remove the critical
time step restriction so that the CFL condition and approximation properties
are balanced in an optimal way, even in the presence of spatial singularities.
