  We present a new compatible finite element advection scheme for the
compressible Euler equations. Unlike the discretisations described in Cotter
and Kuzmin (2016) and Shipton et al (2018), the discretisation uses the
lowest-order family of compatible finite element spaces, but still retains
second-order numerical accuracy. This scheme obtains this second-order accuracy
by first `recovering' the function in higher-order spaces, before using the
discontinuous Galerkin advection schemes of Cotter and Kuzmin (2016). As well
as describing the scheme, we also present its stability properties and a
strategy for ensuring boundedness. We then demonstrate its properties through
some numerical tests, before presenting its use within a model solving the
compressible Euler equations.
