Abstract

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 an accuracy of O(hk) in the energy norm, where k represents the underlying polynomial degree. To validate the approach, a series of numerical experiments had been 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 favorable performance of the current approach.

Original languageEnglish
Pages (from-to)1533-1565
Number of pages33
JournalMathematical Models and Methods in Applied Sciences
Volume34
Issue number8
Early online date30 Apr 2024
DOIs
Publication statusE-pub ahead of print - 30 Apr 2024

Keywords

  • error estimation
  • penalty term
  • positivity preserving
  • Reaction–convection–diffusion equation
  • stabilised finite-element approximation

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics

Cite this