Numerical analysis of a positivity-preserving finite element method for fractional Fisher–KPP equation

Zichen Yao, Zhanwen Yang and Mingying Sun

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 243, issue C, 35-50

Abstract: In this paper, we investigate the numerical analysis of fractional Fisher–KPP equation with Neumann boundary conditions. We rigorously establish key analytical properties of the exact solution, including positivity, boundedness, asymptotic stability, and regularity. A finite element method combined with an L1-implicit–explicit scheme is proposed to solve the equation. Building upon the diagonally positive-definite structure of the mass matrix, it is shown that both the semi-discrete and fully discrete schemes preserve the qualitative properties of the solution, i.e., the numerical solution remains positive for positive initial data, bounded for bounded initial data, and stable for when the exact solution is stable. We further derive the spatial error estimates by exploiting the boundedness and regularity of the exact solution. Our scheme extends effectively to irregular domains while maintaining these properties. Numerical experiments illustrate and complement the theoretical results.

Keywords: Fractional fisher–KPP equation; Finite element method; Positivity-preserving (search for similar items in EconPapers)
Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475425004793
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:243:y:2026:i:c:p:35-50

DOI: 10.1016/j.matcom.2025.11.014

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().