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Numerical analysis of the Brusselator model with Robin boundary conditions

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Abstract

In this paper, we explore the numerical analysis of Brusselator-type reaction-diffusion equations on open bounded convex domains \({\mathfrak {R}} \subset {\mathbb {R}}^{d}\), where \(d \le 3\), with Robin boundary conditions (RBCs). We introduce two finite element schemes: semi-discrete and fully discrete finite element approximations. We demonstrate the existence and uniqueness of solutions for both semi-discrete and fully discrete finite element approximations. Furthermore, we present the convergence of both semi-discrete and fully discrete approximations to the exact solutions. We explore error bounds between semi-discrete and exact solutions, semi-discrete and fully discrete solutions, as well as fully discrete and exact solutions. Additionally, we illustrate the suitable algorithm for solving the fully discrete finite element approximation for each time step.

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Acknowledgements

We express our gratitude to two unnamed reviewers for their insightful comments, which have contributed to enhancements in the manuscript.

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Authors and Affiliations

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

    Ghassan A. Al-Juaifri & Akil J. Harfash

  2. Department of Mathematics, Faculty of Computer Science and Mathematics, University of Kufa, Kufa, Iraq

    Ghassan A. Al-Juaifri

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  1. Ghassan A. Al-Juaifri
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Al-Juaifri, G.A., Harfash, A.J. Numerical analysis of the Brusselator model with Robin boundary conditions. SeMA (2024). https://doi.org/10.1007/s40324-024-00361-9

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