Numerical analysis of a steady Oseen flow problem with frictional type boundary conditions

In this paper, a hemivariational inequality is studied for the steady Oseen fluid flow problem in the presence of a nonsmooth slip boundary condition of friction type. Well-posedness of the Oseen hemivariational inequality is discussed. Mixed finite element methods are introduced to solve the Oseen hemivariational inequality and error estimates are derived for the mixed finite element solutions. The error estimates are of optimal order for low-order mixed element pairs under suitable solution regularity assumptions. Numerical results are reported illustrating the theoretical prediction of convergence orders.