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Abstract : In this paper we study the Stokes problem with some different boundary conditions. We establish a decoupled variational formulation into a system of 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.
Keywords : Stokes equations; A piori and a posteriori errors