Finite element discretization of FSI with distributed Lagrange multiplier
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In this talk I present some recent advances on a fictitious domain approach for the discretization of fluid-structure interaction problems proposed in 2017. This formulation is based on the introduction of a distributed Lagrange multiplier so that the problem fits in the framework of saddle point systems. Our formulation allows for solving the Navier-Stokes equation and the elasticity equation on meshes independent of each other, at the price of computing a coupling term which involves test funtions defined on both meshes. A discussion on how to deal carefully with such term will also be presented. We shall show also that the formulation is robust with respect small cells.