Fluid-structure interaction problems arise in many application fields such as flows around elastic structures or blood flow problems in arteries. The method presented in this paper for solving such a problem is based on a reduction to an equation at the interface, involving the so-called Steklov-Poincare operators. This interface equation is solved by a Newton-like iteration. One step of the Newton-like iteration requires the solution of several decoupled linear subproblems in the structural and the fluid domains. These subproblems are spatially discretized by a finite element method on hybrid meshes. For the time discretization implicit first-order methods are used for both subproblems. The discretized equations are solved by algebraic multigrid methods.
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