A nonstationary mixed hemivariational inequality is studied for an incompressible fluid flow described by the Stokes equations subject to a nonsmooth boundary condition of friction type described by the Clarke subdifferential. The solution existence is shown through a limiting procedure based on temporally semi-discrete approximations. Uniqueness of the solution and its continuous dependence on data are also established. Fully discrete numerical methods are introduced to solve the nonstationary mixed hemivariational inequality. The backward Euler scheme is applied to discretize the time derivative, and mixed finite element methods are used for the spatial discretization. An error bound is derived for the numerical solution of the unknown velocity. Numerical results are reported on computer simulations of some examples.
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