A nodally bound-preserving finite element method for reaction-convection-diffusion equations

2023/11/27 by Abdolreza Amiri, Gabriel R. Barrenechea, Amiri, Abdolreza +3 · 3 citations
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2311.15602

openalex publication_date 2023/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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.

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