  We address the numerical treatment of source terms in algebraic flux
correction schemes for steady convection-diffusion-reaction (CDR) equations.
The proposed algorithm constrains a continuous piecewise-linear finite element
approximation using a monolithic convex limiting (MCL) strategy. Failure to
discretize the convective derivatives and source terms in a compatible manner
produces spurious ripples, e.g., in regions where the coefficients of the
continuous problem are constant and the exact solution is linear. We cure this
deficiency by incorporating source term components into the fluxes and
intermediate states of the MCL procedure. The design of our new limiter is
motivated by the desire to preserve simple steady-state equilibria exactly, as
in well-balanced schemes for the shallow water equations. The results of our
numerical experiments for two-dimensional CDR problems illustrate potential
benefits of well-balanced flux limiting in the scalar case.
