Local projection stabilized method on unsteady Navier-Stokes equations with high Reynolds number using equal order interpolation

In this paper we propose and analyze a stabilized method for unsteady Navier-Stokes equations with high Reynolds number, using local projection stabilized method to control spurious oscillations in the velocities due to dominant convection, or in the pressure due to the velocity-pressure coupling. Using equal-order conforming elements in space and Crank-Nicolson difference in time, we derive a fully discrete formulation. We prove stability and convergence of the approximate solution. The error estimates hold irrespective of the Reynolds number, provided the exact solution is smooth. This result is comparable with the streamline diffusion and continuous interior penalty methods.