  We present a priori error estimates for a multirate time-stepping scheme for
coupled differential equations. The discretization is based on Galerkin methods
in time using two different time meshes for two parts of the problem. We aim at
surface coupled multiphysics problems like two-phase flows. Special focus is on
the handling of the interface coupling to guarantee a coercive formulation as
key to optimal order error estimates.
  In a sequence of increasing complexity, we begin with the coupling of two
ordinary differential equations, coupled heat conduction equation, and finally
a coupled Stokes problem. For this we show optimal multi-rate estimates in
velocity and a suboptimal result in pressure.
  The a priori estimates prove that the multirate method decouples the two
subproblems exactly. This is the basis for adaptive methods which can choose
optimal lattices for the respective subproblems.
