  The NURBS-enhanced finite element method (NEFEM) combined with a hybridisable
discontinuous Galerkin (HDG) approach is presented for the first time. The
proposed technique completely eliminates the uncertainty induced by a
polynomial approximation of curved boundaries that is common within an
isoparametric approach and, compared to other DG methods, provides a
significant reduction in number of degrees of freedom. In addition, by
exploiting the ability of HDG to compute a postprocessed solution and by using
a local a priori error estimate valid for elliptic problems, an inexpensive,
reliable and computable error estimator is devised. The proposed methodology is
used to solve Stokes flow problems using automatic degree adaptation.
Particular attention is paid to the importance of an accurate boundary
representation when changing the degree of approximation in curved elements.
Several strategies are compared and the superiority and reliability of
HDG-NEFEM with degree adaptation is illustrated.
