  Three algebraically stabilized finite element schemes for discretizing
convection-diffusion-reaction equations are studied on adaptively refined
grids. These schemes are the algebraic flux correction (AFC) scheme with Kuzmin
limiter, the AFC scheme with BJK limiter, and the recently proposed Monotone
Upwind-type Algebraically Stabilized (MUAS) method. Both, conforming closure of
the refined grids and grids with hanging vertices are considered. A
non-standard algorithmic step becomes necessary before these schemes can be
applied on grids with hanging vertices. The assessment of the schemes is
performed with respect to the satisfaction of the global discrete maximum
principle (DMP), the accuracy, e.g., smearing of layers, and the efficiency in
solving the corresponding nonlinear problems.
