LAUSR

In this paper a unified nonconforming virtual element scheme for the Navier-Stokes equations with different dimensions and different polynomial degrees is described. Its key feature is the treatment of general elements including non-convex and degenerate elements. According to the properties of an enhanced nonconforming virtual element space, the stability of this scheme is proved based on the choice of a proper velocity and pressure pair. Furthermore, we establish optimal error estimates in the discrete energy norm for velocity and the L2 norm for both velocity and pressure. Finally, we test some numerical examples to validate the theoretical results.