Mathematics

We present some recent results on the finite element approximation of fluid-structure interaction problems. In particular, we consider a new variational formulation of the Immersed Boundary Method (IBM) based on the introduction of a suitable Lagrange multiplier. We prove that a semi-implicit time advancing scheme is unconditionally stable. At each time step we have to solve a saddle point problem. We study existence and uniqueness of the continuous solution and analyze the finite element discretization providing optimal error estimates.