Finite element analysis of the stationary power-law Stokes equations driven by friction boundary conditions

Abstract

In this work, we are concerned with the finite element approximation for the stationary power law Stokes equations driven by nonlinear slip boundary conditions of ‘friction type’. After the formulation of the problem as mixed variational inequality of second kind, it is shown by application of a variant of Babuska– Brezzi’s theory for mixed problems that convergence of the finite element approximation is achieved with classical assumptions on the regularity of the weak solution. Next, solution algorithm for the mixed varia-tional problem is presented and analyzed in details. Finally, numerical simulations that validate the theoret-ical findings are exhibited.