Discrete harmonics for stream function-vorticity Stokes problem

Summary. We consider the bidimensional Stokes problem for incompressible fluids in stream function-vorticity. For this problem, the classical finite element method of degree one converges only in for the norm of the vorticity. We propose to use harmonic functions to approach the vorticity along the boundary. Discrete harmonics are functions that are used in practice to derive a new numerical method. We prove that we obtain with this numerical scheme an error of order for the norm of the vorticity. Received January, 2000 / Revised version received May 15, 2001 / Published online December 18, 2001