As an example for fluid-structure interaction in biomedical problems, the influence of endovascular stent implantation
onto cerebral aneurysm hemodynamics is numerically investigated. The aim is to study the interaction of
the elastic walls of the aneurysm with the geometrical shape of the implanted stent structure for prototypical 2D
configurations. This study can be seen as a basic step towards the understanding of the resulting complex flow
phenomena so that in future aneurysm rupture shall be suppressed by an optimal setting for the implanted stent
geometry. From the mathematical side, numerical techniques for solving the problem of fluid-structure interaction
with an elastic material in a laminar incompressible viscous flow are described. An Arbitrary Lagrangian-Eulerian
(ALE) formulation is employed in a fully coupled monolithic way, considering the problem as one continuum. The
mathematical description and the numerical schemes are designed in such a way that more complicated constitutive
relations (and more realistic for biomechanics applications) for the fluid as well as the structural part can
be easily incorporated. We utilize the well-known Q2P1 finite element pair for discretization in space to gain high
accuracy and perform as time-stepping the 2nd order Crank-Nicholson, resp., Fractional-Step-q -scheme for both
solid and fluid parts. The resulting nonlinear discretized algebraic system is solved by a Newton method which approximates
the Jacobian matrices by the divided differences approach, and the resulting linear systems are solved
by iterative solvers, preferably of Krylov-multigrid type. Preliminary results for the stent-assisted occlusion of
cerebral aneurysm are presented. Since these results are currently restricted to 2D configurations, the aim is not
to predict quantitatively the complex interaction mechanisms between stents and elastic walls of the aneurysm,
but to analyse qualitatively the behaviour of the elasticity of the walls vs. the geometrical details of the stent for
prototypical flow situations.