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.

翻译：本文提出一种新方法，使用协调有限元逼近一类广泛的反应-对流-扩散方程，同时提供满足由底层微分方程给出的物理界限的离散解。本研究的主要结果表明，数值解在能量范数下达到$O(h^k)$阶精度，其中$k$表示底层多项式次数。为验证该方法，针对多种问题实例开展了一系列数值实验。与线性连续内罚稳定化方法以及（分片线性有限元情况下的）代数通量修正方案进行了比较，结果表明本文方法具有更优的性能。