  In this work we develop implicit Active Flux schemes for the scalar advection
equation. At every cell interface we approximate the solution by a polynomial
in time. This allows to evolve the point values using characteristics and to
update the cell averages using fluxes obtained by integrating this polynomial.
The resulting schemes have order of convergence up to five, but show only
moderate oscillations with high frequencies for discontinuous solutions. In
numerical experiments we compare the different methods and show an application
to network flows.
