  We present stability and error analysis for algebraic flux correction schemes
based on monolithic convex limiting. For a continuous finite element
discretization of the time-dependent advection equation, we prove
global-in-time existence and the worst-case convergence rate of 1/2 w.r.t. the
L2 error of the spatial semi-discretization. Moreover, we address the important
issue of stabilization for raw antidiffusive fluxes. Our a priori error
analysis reveals that their limited counterparts should satisfy a generalized
coercivity condition. We introduce a limiter for enforcing this condition in
the process of flux correction. To verify the results of our theoretical
studies, we perform numerical experiments for simple one-dimensional test
problems. The methods under investigation exhibit the expected behavior in all
numerical examples. In particular, the use of stabilized fluxes improves the
accuracy of numerical solutions and coercivity enforcement often becomes
redundant.
