Mixed formulation for interface problems with distributed Lagrange multiplier

We study a mixed formulation for elliptic interface problems which has been recently introduced when dealing with a test problem arising from fluid-structure interaction applications. The formulation, which involves a Lagrange multiplier defined in the solid domain, can be approximated by standard finite elements on meshes which do not need to fit with the interface. In this paper we discuss a modification of the original formulation involving a different approach for the analysis and the numerical implementation of the Lagrange multiplier. New two-dimensional numerical results confirm the good performances of the proposed schemes.