Before revision:  The convergence and stability properties of the approach are studied, firstly, for a benchmark problem of flow around a stationary obstacle and, secondly, for flow around moving obstacles with arising cut cells and fictitious domains .
After revision:  The convergence and stability properties of the algorithm are illustrated in a numerical experiment for an evolving domain. The well-known 2d benchmark of flow around a stationary obstacle and, secondly, for flow around moving obstacles with arising cut cells and fictitious domains .