Convergence results with natural norms: Stabilized Lagrange multiplier method for elliptic interface problems

Abstract

A stabilized Lagrange multiplier method for second order elliptic interface problems is presented in the framework of mortar method. The requirement of LBB (Ladyzhenskaya-Babuška-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.