A Least-Squares Stabilization Virtual Element Method for the Stokes Problem on Polygonal Meshes

Abstract

This paper studies the virtual element method for Stokes problem with a least-squares type stabilization. The method cannot only circumvent the Babuška-Brezzi condition, but also make use of general polygonal meshes, as opposed to more standard triangular grids. Moreover, it is suitable for arbitrary combinations of the velocity and pressure, including equal-order virtual element. We obtain the corresponding energy norm error estimates and $L^2$ norm error estimates for velocity. Finally, a series of numerical experiments are performed to verify the method has good behaviors.