Well-posedness and robust preconditioners for discretized fluid–structure interaction systems

• We formulate the discretized FSI system as saddle point problems.
• We analyze the well-posedness of the FSI saddle point problems.
• We propose optimal preconditioners for FSI discretized systems.

In this paper we develop a family of preconditioners for the linear algebraic systems arising from the arbitrary Lagrangian–Eulerian discretization of some fluid–structure interaction models. After the time discretization, we formulate the fluid–structure interaction equations as saddle point problems and prove the uniform well-posedness. Then we discretize the space dimension by finite element methods and prove their uniform well-posedness by two different approaches under appropriate assumptions. The uniform well-posedness makes it possible to design robust preconditioners for the discretized fluid–structure interaction systems. Numerical examples are presented to show the robustness and efficiency of these preconditioners.