Finite element discretization of the Stokes and Navier – Stokes equations with boundary conditions on the pressure by

We consider the Stokes and Navier--Stokes equations with boundary conditions of Dirichlet type on the velocity on one part of the boundary and involving the pressure on the rest of the boundary. We write the variational formulations of such problems. Next we propose a finite element discretization of them and perform the a priori and a posteriori analysis of the discrete problem. Some numerical experiments are presented in order to justify our strategy.

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