  This work addresses research questions arising from the application of
geometrically exact beam theory in the context of fluid-structure interaction
(FSI). Geometrically exact beam theory has proven to be a computationally
efficient way to model the behavior of slender structures while leading to
rather well-posed problem descriptions. In particular, we propose a
mixed-dimensional embedded finite element approach for the coupling of
one-dimensional geometrically exact beam equations to a three-dimensional
background fluid mesh, referred to as fluid-beam interaction (FBI) in analogy
to the well-established notion of FSI. Here, the fluid is described by the
incompressible isothermal Navier-Stokes equations for Newtonian fluids. In
particular, we present algorithmic aspects regarding the solution of the
resulting one-way coupling schemes and, through selected numerical examples,
analyze their spatial convergence behavior as well as their suitability not
only as stand-alone methods but also for an extension to a full two-way
coupling scheme.
