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International audienceIn this paper, we study the vector penalty-projection method for incompressible unsteady Stokes equations with Dirichlet boundary conditions. The time derivative is approximated by the backward difference formula of second-order scheme (BDF2), namely Gear's scheme, whereas the approximation in space is performed by the finite volume scheme on a Marker And Cell (MAC) grid. After proving the stability of the method, we show that it yields second-error estimates in the time step for both velocity and pressure in the norm of l ∞ (L 2 (Ω)) and l 2 (L 2 (Ω)) respectively. Besides, we show that the splitting error for both velocity and pressure is of order O(√ ε δt) where ε is a penalty parameter chosen as small as desired and δt is the time step. Numerical results in agreement with the theoretical study are also provided

On the error estimates of the vector penalty-projection methods: Second-order scheme