A mixed convergent formulation for the three-dimensional Stokes equations

We consider the three-dimensional Stokes problem in the vorticity-stream fu nction formulation. The computational domain is bounded, polyhedral with a simply connected boundary. A mixed variational formulation based on a split ting of the vorticity into a regular part and a harmonic one is given. We d escribe the associate discrete formulation built on the finite elements des igned by Nedelec. The approach is classical for the regular part, but the h armonic one is treated thanks to a consistent perturbation by penalization of the standard formulation. It leads to an unconditional convergent method . The convergence order is given when the solution is regular. (C) Academie des Sciences/Elsevier, Paris.