A modified nonconforming virtual element with BDM-like reconstruction for the Navier-Stokes equations

In this paper, we develop a modified nonconforming virtual element with a divergence-free BDM-like reconstruction for the Navier-Stokes problem. The main idea is to use a divergence preserving velocity reconstruction operator in the discretization of trilinear and right-hand side terms. The obtained discrete system can not only inherit the advantages of the classical nonconforming virtual element method, i.e., polygonal meshes, a unified discrete scheme, etc, but also achieve the pressure-independence of velocity errors and the effectiveness of small viscosities. Then, we also establish an optimal convergence results for H¹,L²-velocity and L²-pressure. Finally, numerical examples are presented to support the theoretical analysis.