Before revision:  A fully stabilized frame is required for equal order finite elements, both --proper for higher-order-- pressure Poisson stabilization in the bulk of the domain, as well as boundaryzone ]  ] velocity and pressure ghost penalty terms. The present contribution should prove valuable in engineering applications where special emphasis is placed on the optimal effective approximation attaining much smaller relative errors in coarser meshes.
After revision:  A fully stabilized frame is required for equal order finite elements, both --proper for higher-order-- pressure Poisson stabilization in the bulk of the domain, as well as boundaryzone ] ] velocity and pressure ghost penalties defined on faces of cut cells to establish a robust high-order method, in spite of the cell agglomeration technique usually applied on dG methods. The current presentation should prove valuable in engineering applications where special emphasis is placed on the optimal effective approximation attaining much smaller relative errors in coarser meshes.