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This paper focus on numerical approximation of aeroelastic problems. In particular the twodimensional incompressible viscous fluid flow interaction with an elestic structure is considered. The structure motion is described with the aid of nonlinear ordinary differential equations describing either the motion of a flexibly supported airfoil or the motion of a flexibly supported airfoil with a control section. The aerodynamic forces are modelled either by the low-fidelity linearized approach or by high fidelity models based on approximation of these forces based on the evaluated flow quantities. The flow is modelled by the system of Navier-Stokes equations. The time-dependent computational domain is taken into account by the Arbitrary LagrangianEulerian method, where the stabilized finite element method is applied. Numerical results are presented.

Finite Element Approximation of Aeroelastic Problems with Consideration of Nonlinear Effects Due to Large Displacements