Mimetic Spectral Element advection

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.