An H-div finite element method for the Stokes equations on polytopal meshes

In this paper, we introduce an H(div) H(div) finite element method on polygonal and polyhedral meshes for solving the Stokes equations in the primary velocity–pressure formulation. An H(div) H(div) finite element on polygons or polyhedra is introduced to approximate the velocity so that the method is pressure robust and produces exact divergence free solutions, when the discontinuous Pₖ Pk finite element is adopted for the pressure approximation. In addition, this method is stabilizer-free, in handling the H¹ H1 non-conformity. Optimal order error estimates are established for the method. Numerical tests are conducted to confirm the theory.