A distributed lagrange formulation of the finite element immersed boundary method for fluids interacting with compressible solids

We present a distributed Lagrange multiplier formulation of the Finite Element Immersed Boundary Method to couple incompressible fluids with compressible solids. This is a generalization of the formulation presented in Heltai and Costanzo (Comput. Methods Appl. Mech. Eng. 229/232:110–127, 2012), that offers a cleaner variational formulation, thanks to the introduction of distributed Lagrange multipliers, that act as intermediary between the fluid and solid equations, keeping the two formulation mostly separated. Stability estimates and a brief numerical validation are presented.