  A Skeleton-stabilized IsoGeometric Analysis (SIGA) technique is proposed for
incompressible viscous flow problems with moderate Reynolds number. The
proposed method allows utilizing identical finite dimensional spaces (with
arbitrary B-splines/NURBS order and regularity) for the approximation of the
pressure and velocity components. The key idea is to stabilize the jumps of
high-order derivatives of variables over the skeleton of the mesh. For
B-splines/NURBS basis functions of degree $k$ with $C^{\alpha}$-regularity ($0
\leq \alpha < k$), only the derivative of order $\alpha +1$ has to be
controlled. This stabilization technique thus can be viewed as a
high-regularity generalization of the (Continuous) Interior-Penalty Finite
Element Method. Numerical experiments are performed for the Stokes and
Navier-Stokes equations in two and three dimensions. Oscillation-free solutions
and optimal convergence rates are obtained. In terms of the sparsity pattern of
the algebraic system, we demonstrate that the block matrix associated with the
stabilization term has a considerably smaller bandwidth when using B-splines
than when using Lagrange basis functions, even in the case of $C^0$-continuity.
This important property makes the proposed isogeometric framework practical
from a computational effort point of view.
