Before revision:  This approach combines the best from both worlds, firstly the advantages of a piece-wise discontinuous high--order accurate approximation and secondly the advantages of an unfitted to the true geometry grid around possibly complex objects and/or geometrical deformations.
After revision:  This approach combines the best from both worlds, firstly the advantages of a piece-wise discontinuous high-order accurate approximation and secondly the advantages of an unfitted to the true geometry grid around possibly complex objects and/or geometrical deformations.