Abstract
In this paper we address the problem of the numerical approximation of the incompressible flow around a vibrating airfoil. The robust higher order finite element method (FEM) for incompressible flow approximation is presented. The method is based on the combination of several techniques, e.g., the Arbitrary Lagrangian-Eulerian formulation of the Navier-Stokes equations, the stabilization of the finite element scheme and the linearization of the discrete nonlinear problem. The main attention is paid to the proper stabilization of the higher order finite element method applied on incompressible flow problems. The stabilization procedure based on Galerkin Least-Squares (GLS) method is discussed. The numerical results are presented.
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