New finite element methods in computational fluid dynamics by H(div) elements

In this paper, the authors present two formulations for the Stokes problem which make use of the existing H(div) elements of the Raviart-Thomas type originally developed for the second-order elliptic problems. In addition, two new H(div) elements are constructed and analyzed particularly for the new formulations. Optimal-order error estimates are established for the corresponding finite element solutions in vaxious Sobolev norms. The finite element solutions feature a full satisfaction of the continuity equation when existing Raviart-Thomas-type elements are employed in the numerical scheme.