## Section: Scientific Foundations

### Finite element methods for interface problems

The NXFEM (Nitsche eXtended finite element method) has been developed in [63] and [64] . It is based on a pure variational formulation with standard finite element spaces, which are locally enriched in such a way that the accurate capturing of an interface not aligned with the underlying mesh is possible, giving a rigorous formulation of the very popular XFEM. A typical computation for the Stokes problem with varying, piecewise constant viscosity is shown in Figure 1 . This technology opens the door to many applications in the field of fluid mechanics, such as immiscible flows, free surface flows and so on.