Virtual Elements for the Navier-Stokes problem on polygonal meshes

摘要

A family of Virtual Element Methods for the 2D Navier-Stokes equations isproposed and analysed. The schemes provide a discrete velocity field which ispoint-wise divergence-free. A rigorous error analysis is developed, showingthat the methods are stable and optimally convergent. Several numerical testsare presented, confirming the theoretical predictions. A comparison with somemixed finite elements is also performed.