Local projection type stabilization applied to inf–sup stable discretizations of the Oseen problem

The one- and two-level local projection methods are applied to inf–sup stable discretizations of the Oseen problem. Error bounds of order r are proved for known inf–sup stable pairs of finite element spaces which approximate velocity and pressure by elements of order r and r−1, respectively. New families of inf–sup stable finite element spaces are proposed which approximate velocity and pressure by different elements, being both of order r. In the small viscosity case, an improved error estimate of order r+1/2 is shown. Numerical results confirm the theoretical convergence results.