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

Amiri, Abdolreza and Barrenechea, Gabriel R. and Pryer, Tristan (2024) A nodally bound-preserving finite element method for reaction-convection-diffusion equations. Mathematical Models and Methods in Applied Sciences, 34 (08). pp. 1533-1565. ISSN 0218-2025 (https://doi.org/10.1142/S0218202524500283)

[thumbnail of Amiri-etal-MMMAS-2024-A-nodally-bound-preserving-finite-element-method]
Preview
 Text. Filename: Amiri-etal-MMMAS-2024-A-nodally-bound-preserving-finite-element-method.pdf
Final Published Version
License: Creative Commons Attribution 4.0 logo
Download (5MB)| Preview

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 (ℎ) in the energy norm, where 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.

ORCID iDs

Amiri, Abdolreza, Barrenechea, Gabriel R. ORCID logoORCID: https://orcid.org/0000-0003-4490-678X and Pryer, Tristan;
  • Item type:Article
    ID code:89130
    Dates:
    Date
    Event
    1 July 2024
    Published
    30 April 2024
    Published Online
    20 February 2024
    Accepted
    16 May 2023
    Submitted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:07 May 2024 09:57
    Last modified:11 Nov 2024 14:15
    URI:https://strathprints.strath.ac.uk/id/eprint/89130
CORE (COnnecting REpositories)