Finite element analysis for Stokes and Navier-Stokes equations driven by threshold slip boundary conditions

Abstract

This paper is devoted to the study of finite element approximations of variational inequalities with a special nonlinearity coming from boundary conditions. After re-writing the problems in the form of variational inequalities, a fixed point strategy is used to show existence of solutions. Next we prove that the finite element approximations for the Stokes and Navier Stokes equations converge respectively to the solutions of each continuous problems. Finally, Uzawa’s algorithm is formulated and convergence of the procedure is shown, and numerical validation test is achieved.