  A stabilized Lagrange multiplier method for second order elliptic interface
problems is presented in the framework of mortar method. The requirement of LBB
(Ladyzhenskaya-Babu\v{s}ka-Brezzi) condition for mortar method is alleviated by
introducing penalty terms in the formulation. Optimal convergence results are
established in natural norm which is independent of mesh. Numerical experiments
are conducted in support of the theoretical derivations.
