  Analysis of an interface stabilised finite element method for the scalar
advection-diffusion-reaction equation is presented. The method inherits
attractive properties of both continuous and discontinuous Galerkin methods,
namely the same number of global degrees of freedom as a continuous Galerkin
method on a given mesh and the stability properties of discontinuous Galerkin
methods for advection dominated problems. Simulations using the approach in
other works demonstrated good stability properties with minimal numerical
dissipation, and standard convergence rates for the lowest order elements were
observed. In this work, stability of the formulation, in the form of an inf-sup
condition for the hyperbolic limit and coercivity for the elliptic case, is
proved, as is order $k+1/2$ order convergence for the advection-dominated case
and order $k+1$ convergence for the diffusive limit in the $L^{2}$ norm. The
analysis results are supported by a number of numerical experiments.
