On stabilized equal-order virtual element methods for the Navier-Stokes equations on polygonal meshes

This paper studies non-inf-sup stable virtual element methods for the Navier-Stokes problems based on "equal-order" virtual elements. Two equivalent pressure stabilizations are considered, which contain neither second-order derivative terms nor extra coupling terms. In addition, the methods are parameter-free. We obtain optimal error estimations in the H1-norm for velocity and the L2-norm for velocity and pressure. Several numerical experiments in two-dimension for different polynomial degrees and different polygonal meshes are offered which certify the theoretical results and display excellent stability.