Advance Access publication on November 19, 2013 Conforming and divergence-free Stokes elements in three dimensions

Conforming finite element pairs for the three-dimensional Stokes problem on general simplicial trian-gulations 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 diver-gence operator maps the velocity space into the space of piecewise constants. Consequently, the method produces exactly divergence-free velocity approximations