In this paper, we propose and analyze a local projection stabilization virtual element method for steady scalar convection-diffusion-reaction problem in the convective-dominated regime. Stability and optimal convergence property in the convective-dominated regime are proven in a suitable norm. Numerical results show that the proposed method is stable at very large Reynolds number and is in good agreement with the expected rate of convergence.

中文翻译：

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对流-扩散-反应方程的局部投影稳定虚元方法

在本文中，我们提出并分析了一种局部投影稳定虚拟元方法，用于解决对流占主导地位的稳定标量对流-扩散-反应问题。以合适的范数证明了对流主导体制中的稳定性和最佳收敛特性。数值结果表明，所提出的方法在非常大的雷诺数下是稳定的，并且与预期的收敛速度非常吻合。