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.

中文翻译：

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求解图案形成中具有和不具有交叉扩散的非均匀布鲁塞尔模型的虚拟元方法

虚拟单元法 (VEM) 是一项最新技术，它可以利用非常通用的多边形/多面体网格，而无需在单元上集成复杂的非多项式函数并保持最佳收敛顺序。在本文中，对 VEM 进行了公式化和分析，以解决多边形网格上的 Brusselator 模型。还导出了最佳先验误差估计（在小数据假设下）。进行了大量数值实验以验证所提出方案的准确性和效率，并在一组不同的计算网格上绘制布鲁塞尔方程的图灵模式。