Penalty-Free Nitsche Method for Interface Problems

Nitsche's method is a penalty-based method to weakly enforce boundary conditions in the finite element method. In this paper, we present a penalty free version of Nitsche's method to impose interface coupling in the framework of unfitted domain decomposition. Unfitted domain decomposition is understood in the sense that the interface between the domains can cross elements of the mesh arbitrarily. The pure diffusion problem with discontinuous material parameters is considered for the theoretical study, we show the convergence of the L-2 and H-1-error for high contrast in the diffusivities. Then, we give the corresponding numerical results for the pure diffusion problem, additionally we consider the Stokes problem. We compare the performance of the penalty free method with the more classical symmetric and nonsymmetric Nitsche's methods for different cases, including for the error generated in the interface fluxes.