Stabilized finite elements for transient flow problems on varying spatial meshes

Changing the spatial mesh in transient flow computations may negatively affect the pressure on the new mesh due to the fact that the interpolated or L 2 -projected velocities usually violate the divergence constraint on the new mesh. It is proven that this pressure perturbation scales as k - 1 when k denotes the time step. Hence, this phenomenon becomes increasingly relevant for small time steps. This is even more important due to the fact that this phenomena occurs independently whether the discrete scheme is inf-sup stable or not. In order to solve this problem, a divergence free projection should be applied instead of a simple interpolation or L 2 -projection of the velocities. For inf–sup stable finite elements, a recent published analysis shows how such a projection should be performed. For non inf-sup stable finite element pairs with stabilization techniques, as for instance equal-order elements, such an analysis is still missing. In this work, we tackle this problem, present a possible algorithm and prove bounds of the pressure in the linear Stokes case. The type of pressure stabilization is very general and includes the interior penalty method, local projection techniques and others.