Low order nonconforming mixed finite element method for nonstationary incompressible Navier-Stokes equations

摘要

This paper studies a low order mixed finite element method(FEM) for nonstationary incompressible Navier-Stokes equations.The velocity and pressure are approximated by the nonconforming constrained Q^(rot)_1 element and the piecewise constant,respectively.The superconvergent error estimates of the velocity in the broken H^1-norm and the pressure in the L^2-norm are obtained respectively when the exact solutions are reasonably smooth.A numerical experiment is carried out to confirm the theoretical results.