On a finite element approximation of the Stokes equations under a slip boundary condition of the friction type

A finite element approximation of the Stokes equations under a certain nonlinear boundary condition, namely, the slip boundary condition of friction type, is considered. We propose an approximate problem formulated by a variational inequality, prove an existence and uniqueness result, present an error estimate, and discuss a numerical realization using an iterative Uzawa-type method. Several numerical examples are provided to support our theoretical results.