A priori and a posteriori estimates for three-dimensional Stokes equations with non standard boundary conditions

In this paper we study the Stokes problem with some non standard boundary conditions. The variational formulation decouples into a system velocity and a Poisson equation for the pressure. The continuous and corresponding discrete system do not need an inf-sup condition. Hence, the velocity is approximated with curl conforming finite elements and the pressure with standard continuous elements. Next, we establish optimal a priori and a posteriori estimates and we finish this paper with numerical tests.