A second-order finite element variational multiscale scheme for the fully discrete unsteady Navier-Stokes equations (Q1786944)

The authors present a fully discrete finite element variational multiscale scheme for the unsteady incompressible N-S equations where large Reynolds numbers are allowed. In authors' words: ``the scheme uses conforming finite element pairs for partial discretization and a three-point difference formula for temporal discretization which is of second-order, where a stabilization term based on two local Gauss integrations is employed''. The authors prove stability of the scheme, derive a priori estimates, an give some numerical results to illustrate the theoretical results.