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, 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.
@article{arxiv.1304.6926,
title = {Mimetic Spectral Element advection},
author = {Artur Palha and Pedro Pinto Rebelo and Marc Gerritsma},
journal= {arXiv preprint arXiv:1304.6926},
year = {2013}
}