A mixed finite element method for 3D Navier-Stokes equations

The considered finite element method represents the exact generalization to the three-dimensional case of the (phi, omega) method introduced in the two-dimensional case by Glowinski (1973) and Ciarlet and Raviart (1974). A particular case is presented of a general family of finite elements using polynomials of degree k. In the general case, error estimates in h to the (k-1) power are proved. There exist also two families of finite elements conforming in H(rot) and H(div), respectively, which are associated to cubes.