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We present a distributed Lagrange multiplier formulation of the FiniteElement Immersed Boundary Method to couple incompressible fluids withcompressible solids. This is a generalization of the formulation presented inHeltai and Costanzo (2012), that offers a cleaner variational formulation,thanks to the introduction of distributed Lagrange multipliers, that acts asintermediary between the fluid and solid equations, keeping the two formulationmostly separated. Stability estimates and a brief numerical validation arepresented.

A distributed Lagrange formulation of the Finite Element Immersed Boundary Method for fluids interacting with compressible solids