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Three algebraically stabilized finite element schemes for discretizingconvection-diffusion-reaction equations are studied on adaptively refinedgrids. These schemes are the algebraic flux correction (AFC) scheme with Kuzminlimiter, the AFC scheme with BJK limiter, and the recently proposed MonotoneUpwind-type Algebraically Stabilized (MUAS) method. Both, conforming closure ofthe refined grids and grids with hanging vertices are considered. Anon-standard algorithmic step becomes necessary before these schemes can beapplied on grids with hanging vertices. The assessment of the schemes isperformed with respect to the satisfaction of the global discrete maximumprinciple (DMP), the accuracy, e.g., smearing of layers, and the efficiency insolving the corresponding nonlinear problems.

Adaptive Grids in the Context of Algebraic Stabilizations for Convection-Diffusion-Reaction Equations