  This paper introduces a novel approach to approximate a broad range of
reaction-convection-diffusion equations using conforming finite element methods
while providing a discrete solution respecting the physical bounds given by the
underlying differential equation. The main result of this work demonstrates
that the numerical solution achieves accuracy of $O(h^k)$ in the energy norm,
where $k$ represents the underlying polynomial degree. To validate the
approach, a series of numerical experiments is conducted for various problem
instances. Comparisons with the linear continuous interior penalty stabilised
method, and the algebraic flux-correction scheme (for the piecewise linear
finite element case) have been carried out, where we can observe the favourable
performance of the current approach.

Numerical Analysis;Numerical Analysis