  We consider a boundary value problem for the stationary Stokes problem and
the corresponding pressure-Poisson equation. We propose a new formulation for
the pressure-Poisson problem with an appropriate additional boundary condition.
We establish error estimates between solutions to the Stokes problem and the
pressure-Poisson problem in terms of the additional boundary condition. As
boundary conditions for the Stokes problem, we use a traction boundary
condition and a pressure boundary condition introduced in C. Conca et al
(1994).
