A penalty-FEM for navier-stokes type variational inequality with nonlinear damping term

In this article, we consider a penalty finite element (FE) method for incompressible Navier-Stokes type variational inequality with nonlinear damping term. First, we establish penalty variational formulation and prove the well-posedness and convergence of this problem. Then we show the penalty FE scheme and derive some error estimates. Finally, we give some numerical results to verify the theoretical rate of convergence. (c) 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 918-940, 2017