On spurious velocities in incompressible flow problems with interfaces

We show that a non-physical velocity may appear in the finite element calculation of incompressible two-phase flows subjected to an external local force. There are different sources responsible for this phenomenon: approximation of the incompressibility constraint, the interface, and the local external force. Furthermore, we demonstrate that this non-physical velocity does not vanish with the expected order of convergence. We evaluate different concepts and give recommendations for a proper handling of this phenomenon.