In this article, using the weighted discrete least-squares, we propose a patch reconstruction finite element space with only one degree of freedom per element. As the approximation space, it is applied to the discontinuous Galerkin methods with the upwind scheme for steady-state convection-diffusion-reaction problems over polytopic meshes. The optimal error estimates are proved in both diffusion-dominated and convection-dominated regimes. Finally, several numerical experiments are presented to verify the error estimates, and further to well approximate boundary layers and/or internal layers.

中文翻译：

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多面网格上对流-扩散-反应问题的补丁重建的不连续伽辽金方法

在本文中，使用加权离散最小二乘法，我们提出了一个补丁重建有限元空间，每个元素只有一个自由度。作为近似空间，它被应用于多面网格上稳态对流-扩散-反应问题的逆风方案的不连续伽辽金方法。在扩散主导和对流主导的情况下都证明了最佳误差估计。最后，提出了几个数值实验来验证误差估计，并进一步很好地近似边界层和/或内部层。