A Divergence Free Weak Virtual Element Method for the Stokes Problem on Polytopal Meshes

Some virtual element methods on polytopal meshes for the Stokes problem are proposed and analyzed. The pressure is approximated by discontinuous polynomials, while the velocity is discretized by H(div) virtual elements enriched with some tangential polynomials on the element boundaries. A weak symmetric gradient of the velocity is computed using the corresponding degree of freedoms. The main feature of the method is that it exactly preserves the divergence free constraint, and therefore the error estimates for the velocity does not explicitly depend on the pressure.