Abstract
In this work, a finite element approximation of the Stokes problem under a slip boundary condition of friction type, known as the Tresca boundary condition, is considered. We treat the approximate problem of a four field mixed formulation using the P-1-bubble element for the velocity field, P-1 element for the pressure field and the P-1 element for the Lagrange multipliers lambda(n) and lambda(t) defined on the slip boundary. The multiplier lambda(t) is introduced to regularize the non-differentiable problem, whereas lambda(n) treats the impermeability condition. Existence and uniqueness results for both continuous and discrete problems are proven and an a priori error estimate is established. Numerical realization of such problem is discussed and some numerical tests are provided.