Fully discrete nonconforming finite element schemes for the nonstationary Navier-Stokes equations

Fully discrete approximations to the solution of the incompressible Navier-Stokes equations are introduced and analyzed. Standard elements are used for the pressure approximation, while nonconforming finite clement spaces are used for the velocity approximation. These elements are discontinuous across interelement boundaries and satisfy the incompressibility condition pointwise on each 'triangle'. Implicit Runge-Kutta methods are used for the temporal discretizations. The spatial grids are allowed to change from one time level to the next. Optimal order error estimates are proved for the approximations of velocity and pressure.