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Virtual Element Method for Solving an Inhomogeneous Brusselator Model With and Without Cross-Diffusion in Pattern Formation

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Abstract

The virtual element method (VEM) is a recent technology that can make use of very general polygonal/polyhedral meshes without the need to integrate complex nonpolynomial functions on the elements and preserving an optimal order of convergence. In this article, the VEM is formulated and analyzed to solve the Brusselator model on polygonal meshes. Also an optimal a priori error estimate (under a small data assumption) is derived. Ample numerical experiments are performed to validate the accuracy and efficiency of the proposed scheme and to plot the Turing patterns of the Brusselator equation on a set of different computational meshes.

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Acknowledgements

The authors are very grateful to two reviewers for carefully reading this paper and for their comments and suggestions, which have improved the paper.

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  1. Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424, Hafez Ave., 15914, Tehran, Iran

    Mehdi Dehghan & Zeinab Gharibi

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  1. Mehdi Dehghan
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  2. Zeinab Gharibi
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Correspondence to Mehdi Dehghan.

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Dehghan, M., Gharibi, Z. Virtual Element Method for Solving an Inhomogeneous Brusselator Model With and Without Cross-Diffusion in Pattern Formation. J Sci Comput 89, 16 (2021). https://doi.org/10.1007/s10915-021-01626-5

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