Divergence Free VEM for the Stokes Problem with No Internal Degrees of Freedom

In the present contribution we concentrate on fluid mechanics and present a “super-reduced” version of the VEM scheme introduced in previous papers by the same authors for the Navier-Stokes equation, here focusing on the simpler Stokes problem. The basic advantage of the method is, in addition to the capability of handling general polytopal meshes, the property of delivering a truly divergencefree velocity solution. In addition, it exists a reduced version of the method with a smaller pressure and velocity space, but still holding the same accuracy. In this short contribution we briefly review the above mentioned VEM method and introduce a further reduction to the velocity space, leading to a scheme with velocity degrees of freedom only on the element boundaries.