On the connection between the stabilized Lagrange multiplier and Nitsche’s methods

We derive Nitsche’s method for the domain decomposition through the stabilized Lagrange multiplier method. Taking material parameters carefully into account this derivation naturally introduces parameter weighted average flux and stabilizing terms to Nitsche’s method. We show stability and a priori analyses in the mesh dependent norms for both the stabilized method and Nitsche’s method, and discuss connections between the proposed methods.