Two-grid MFEAs for the incompressible Stokes type variational inequality with damping

In this paper, we study two-grid mixed finite element algorithms (MFEAs) for the stationary incompressible Stokes equations with damping and nonlinear slip boundary conditions. We set up the weak formulation and obtain the well-posedness. Then employing the mixed finite element method, some optimal error estimates between the exact solution and the approximation solution are derived. Two kinds of two-grid MFEAs based on the Stokes correction and Newton-type correction are established. Some error estimates for two-grid MFEAs are obtained. Several numerical results are presented to confirm our theoretical findings.