Pressure-independent velocity error estimates for (Navier-)Stokes nonconforming virtual element discretization with divergence free

In this paper, we propose a divergence-free nonconforming virtual element discrete scheme for (Navier-) Stokes problem based on Raviart-Thomas-like virtual element space. By choosing different (compared to Zhao et al. (SIAM J. Numer. Anal. 57, 2730–2759, 2019)) degrees of freedom and global virtual element space, we realize H¹- and L²-error estimates of the velocity that are independent of the continuous pressure. Moreover, the presented scheme can also deal with polygonal meshes (including non-convex and degenerate elements), arbitrary approximation orders k, and large Reynolds numbers. Finally, we investigate several classical numerical experiments of the incompressible flow to present the performance of this numerical scheme.