An efficient finite element method for embedded interface problems

A stabilized finite element method based on the Nitsche technique for enforcing constraints leads to an efficient computational procedure for embedded interface problems. We consider cases in which the jump of a field across the interface is given, as well as cases in which the primary field on the interface is given. The finite element mesh need not be aligned with the interface geometry. We present closed-form analytical expressions for interfacial stabilization terms and simple procedures for accurate flux evaluations. Representative numerical examples demonstrate the effectiveness of the proposed methodology.