  A unique set of correction functions for Flux Reconstruction is presented,
with there derivation stemming from proving the existence of energy stability
in the Lebesgue norm. The set is shown to be incredibly arbitrary with the only
union to existing correction function sets being show to be for DG. Von Neumann
analysis of both advection and coupled advection-diffusion is used to show that
once coupled to a temporal integration method, good CFL performance can be
achieved and the correction function may have better dispersion and dissipation
for application to implicit LES. Lastly, the turbulent Taylor-Green vortex test
case is then used to show that correction functions can be found that improve
the accuracy of the scheme when compared to the error levels of Discontinuous
Galerkin.
