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D. Boffi, L. Gastaldi, M. Ruggeri:
"Mixed formulation for interface problems with distributed Lagrange multiplier";
Computers and Mathematics with Applications, 68 (2014), 12; S. 2151 - 2166.

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.

interface problems, finite elements, fluid-structure interaction, Lagrange multiplier

http://dx.doi.org/10.1016/j.camwa.2014.07.020