  We provide a framework for high-order discretizations of nonlinear scalar
convection-diffusion equations that satisfy a discrete maximum principle. The
resulting schemes can have arbitrarily high order accuracy in time and space,
and can be stable and maximum-principle-preserving (MPP) with no step size
restriction. The schemes are based on a two-tiered limiting strategy, starting
with a high-order limiter-based method that may have small oscillations or
maximum-principle violations, followed by an additional limiting step that
removes these violations while preserving high order accuracy. The desirable
properties of the resulting schemes are demonstrated through several numerical
examples.
