A new unfitted stabilized Nitsche's finite element method for Stokes interface problems

In this paper, we introduce and analyze a new stabilized finite element method based on combining Nitsche's method with a ghost penalty method for two-phase Stokes flows involving two different kinematic viscosities by using the lowest equal order velocity-pressure pairs. The interface between two-phase flows does not need to align with the mesh and interface conditions are imposed weakly using a Nitsche type approach. This method has some prominent features: parameter-free, avoiding calculation of higher order derivatives or edge data structures and stabilization being completely local behavior about pressure. We prove that the method is inf-sup stable and obtain optimal order a priori error estimates. We also show that the estimate for the condition number of the stiffness matrix is independent of the location of the interface. Finally, we present some numerical examples to support our theoretical results.