Virtual Elements for the Navier--Stokes Problem on Polygonal Meshes

A family of virtual element methods for the two-dimensional Navier--Stokes equations is proposed and analyzed. The schemes provide a discrete velocity field which is pointwise divergence-free. A rigorous error analysis is developed, showing that the methods are stable and optimally convergent. Several numerical tests are presented, confirming the theoretical predictions. A comparison with some mixed finite elements is also...