  Immersed finite element methods generally suffer from conditioning problems
when cut elements intersect the physical domain only on a small fraction of
their volume. De Prenter et al. [Computer Methods in Applied Mechanics and
Engineering, 316 (2017) pp. 297-327] present an analysis for symmetric positive
definite (SPD) immersed problems, and for this class of problems an algebraic
preconditioner is developed. In this contribution the conditioning analysis is
extended to immersed finite element methods for systems that are not SPD and
the preconditioning technique is generalized to a connectivity-based
preconditioner inspired by Additive-Schwarz preconditioning. This
Connectivity-based Additive-Schwarz (CbAS) preconditioner is applicable to
problems that are not SPD and to mixed problems, such as the Stokes and
Navier-Stokes equations. A detailed numerical investigation of the effectivity
of the CbAS preconditioner to a range of flow problems is presented.
