VIRTUAL ELEMENT APPROXIMATIONS FOR NON-STATIONARY NAVIER-STOKES EQUATIONS ON POLYGONAL MESHES

This article deals with the development of virtual element methods for the approximation of non-stationary Navier-Stokes equation. The proposed lowest order virtual element spaces for velocity and pressure are constructed in such a way that the inf-sup conditions holds, and easy to implement in comparison with other pair of spaces which satisfy the inf-sup condition. For time discretization, the backward Euler scheme is employed, and both semi and fully discrete schemes are discussed and analyzed. With the help of certain projection operators, error estimates are established in suitable norms for both semi and fully discretized schemes. Moreover, several numerical experiments are conducted to verify the theoretical rate of convergence and to observe the computational efficiency of the proposed schemes.