| Abstract: | We present a projection scheme whose end‐of‐step velocity is locally pointwise divergence free, using a continuous ?1 approximation for the velocity in the momentum equation, a first‐order Crouzeix–Raviart approximation at the projection step, and a ?0 approximation for the pressure in both steps. The analysis of the scheme is done only for grids that guarantee the existence of a divergence free conforming ?1 interpolant for the velocity. Optimal estimates for the velocity error in L2‐ and H1‐norms are deduced. The numerical results demonstrate that these estimates should also hold on grids on which the continuous ?1 approximation for the velocity locks. Since the end‐of‐step velocity is locally solenoidal, the scheme is recommendable for problems requiring good mass conservation. Copyright © 2005 John Wiley & Sons, Ltd. |
