Finite element analysis of cross-diffusion three-species Shigesada-Kawasaki-Teramoto model

Document Type : Research Article

Authors

Ghufran A. Al-Musawi ¹

Huda A. Challoob ²

Akil Jassim Harfash ²

¹ Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq.

² Department of Mathematics, College of Sciences, University of Basrah, Basrah, Iraq.

10.22067/ijnao.2025.95757.1742

Abstract

In this study, a three-species Shigesada-Kawasaki-Teramoto (SKT) model was studied numerically using the finite element method (FEM). The first step is to introduce the regularised problem to the original problem. After that, some bounds of the solution to the regularised problem are found in various spaces, which is considered the basic step to start the study. The regularised problem is approximated using FEM, and then the existence of the solution to the approximate problem is proven. Also, the approximate solutions' bounds will be found, and their spaces can be determined using these bounds. After that, the convergence of the approximate solutions to the exact solutions will be studied, and these findings will be followed by an examination of how the weak form of the approximate problem converges to the continuous weak form. Thus, the existence of the solutions of the SKT model will be proven. Finally, the algorithm for the approximate problem will be presented, and the numerical results will be introduced.

Keywords

Finite element

Shigesada-Kawasaki-Teramoto

Convergence

Weak solution

Subjects

• Numerical methods for differential equations and its applications

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