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 divergencefree 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 H-1, L-2-velocity and L-2-pressure. Finally, numerical examples are presented to support the theoretical analysis. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.

Automated summary

In this paper, a modified nonconforming virtual element method with a divergence-free BDM-like reconstruction for the Navier-Stokes problem is developed. The new method uses a divergence preserving velocity reconstruction operator to achieve velocity error independence of pressure and effectiveness of small viscosities. Optimal convergence results for H-1, L-2-velocity, and L-2-pressure are established, and numerical examples support the theoretical analysis.