  In this work, a multirate in time approach resolving the different time
scales of a convection-dominated transport and coupled fluid flow is developed
and studied in view of goal-oriented error control by means of the Dual
Weighted Residual (DWR) method. Key ingredients are an arbitrary degree
discontinuous Galerkin time discretization of the underlying subproblems, an a
posteriori error representation for the transport problem coupled with flow and
its implementation using space-time tensor-product spaces. The error
representation allows the separation of the temporal and spatial discretization
error which serve as local error indicators for adaptive mesh refinement. The
performance of the approach and its software implementation are studied by
numerical convergence examples as well as an example of physical interest for
convection-dominated transport.
