  We present a discretization of the linear advection of differential forms on
bounded domains. The framework previously established is extended to
incorporate the Lie derivative, $\mathcal L$, by means of Cartan's homotopy
formula. The method is based on a physics-compatible discretization with
spectral accuracy . It will be shown that the derived scheme has spectral
convergence with local mass conservation. Artificial dispersion depends on the
order of time integration.
