Conforming and divergence-free Stokes elements in three dimensions

Conforming finite element pairs for the three-dimensional Stokes problem on general simplicial triangulations are constructed. The pressure space simply consists of piecewise constants, whereas the velo-city space consists of cubic polynomials augmented with rational functions. We show the existence of a bounded Fortin projection and therefore the necessary LBB condition is satisfied. In addition, the divergence operator maps the velocity space into the space of piecewise constants. Consequently, the method produces exactly divergence-free velocity approximations.