  We present a space-time continuous-Galerkin finite element method for solving
incompressible Navier-Stokes equations. To ensure stability of the discrete
variational problem, we apply ideas from the variational multi-scale method.
The finite element problem is posed on the ``full" space-time domain,
considering time as another dimension. We provide a rigorous analysis of the
stability and convergence of the stabilized formulation. And finally, we apply
this method on two benchmark problems in computational fluid dynamics, namely,
lid-driven cavity flow and flow past a circular cylinder. We validate the
current method with existing results from literature and show that very large
space-time blocks can be solved using our approach.
