  We examine a variational multiscale method in which the unresolved
fine-scales are approximated element-wise using a discontinuous Galerkin
method. We establish stability and convergence results for the methodology as
applied to the scalar transport problem, and we prove that the method exhibits
optimal convergence rates in the SUPG norm and is robust with respect to the
Peclet number if the discontinuous subscale approximation space is sufficiently
rich. We apply the method to isogeometric NURBS discretizations of steady and
unsteady transport problems, and the corresponding numerical results
demonstrate that the method is stable and accurate in the advective limit even
when low-order discontinuous subscale approximations are employed.
