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- Title
A nodally bound-preserving finite element method for reaction–convection–diffusion equations.
- Authors
Amiri, Abdolreza; Barrenechea, Gabriel R.; Pryer, Tristan
- 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 (h k) 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.
- Subjects
TRANSPORT equation; FINITE element method; DIFFERENTIAL equations; EQUATIONS
- Publication
Mathematical Models & Methods in Applied Sciences, 2024, Vol 34, Issue 8, p1533
- ISSN
0218-2025
- Publication type
Article
- DOI
10.1142/S0218202524500283