Finite element method for a stationary Stokes hemivariational inequality with slip boundary condition

Abstract

Abstract This paper is devoted to the study of a hemivariational inequality problem for the stationary Stokes equations with a nonlinear slip boundary condition. The hemivariational inequality is formulated with the use of the generalized directional derivative and generalized gradient in the sense of Clarke. We provide an existence and uniqueness result for the hemivariational inequality. Then we apply the finite element method to solve the hemivariational inequality. The incompressibility constraint is treated through a mixed formulation. Error estimates are derived for numerical solutions. Numerical simulation results are reported to illustrate the theoretically predicted convergence orders.