  In this paper we consider stabilised finite element methods for hyperbolic
transport equations without coercivity. Abstract conditions for the convergence
of the methods are introduced and these conditions are shown to hold for three
different stabilised methods: the Galerkin least squares method, the continuous
interior penalty method and the discontinuous Galerkin method. We consider both
the standard stabilisation methods and the optimisation based method introduced
in \cite{part1}. The main idea of the latter is to write the stabilised method
in an optimisation framework and select the discrete function for which a
certain cost functional, in our case stabilisation term, is minimised. Some
numerical examples illustrate the theoretical investigations.
