  In this paper a novel application of the (high-order)
$H(\text{div})$-conforming Hybrid Discontinuous Galerkin finite element method
for monolithic fluid-structure interaction (FSI) is presented. The Arbitrary
Lagrangian Eulerian (ALE) description is derived for $H(\text{div})$-conforming
finite elements including the Piola transformation, yielding exact divergence
free fluid velocity solutions. The arising method is demonstrated by means of
the benchmark problems proposed by Turek and Hron [50]. With hp-refinement
strategies singularities and boundary layers are overcome leading to optimal
spatial convergence rates.
