Approximation of bingham's variational inequalities by a penalty function for the incompressibility constraint

Limiting ourselves to a case where there is a unique solution for Bingham's inequality, we introduce a penalization on the constraint ∇.u = 0. We show that the solution uε of the pertubated problem converges to the solution u of the original one in 0(ε). The techniques we use allow us to justify a fixed point algorithm for the nonlinearity due to the Navier-Stokes operator and used for finite element approximations of the original problem.