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 the steady-state convection-diffusion-reaction problems over polytopic meshes. The optimal error estimates are provided in both diffusion-dominated and convection-dominated regimes. Furthermore, several numerical experiments are presented to verify the theoretical error estimates, and to well approximate boundary layers and/or internal layers.
翻译：在本篇文章中,我们使用加权离散最小方块,建议对每个元素只有一度自由的限定空间进行补丁重建。作为近似空间,它应用到不连续的Galerkin方法,在多位元模上方稳定状态对流-扩散-反应问题上风方案上风方案上方方法上方方法上方方法上方方法上方方法上方方法上方方法上方方法上方方法上方方法上方方法上方方法上方方法上方方法上方方法上方方法上方方法上方方法上方方法上方方法上方方法上方方法上方方法上方方法上方方法上方方法上方方法上方方法上方方法上方方法上,最佳误差估计方法是在以扩散为主和对流为主的系统中进行。此外,还进行了若干数字实验,以核实理论误差估计数,并大致接近边界层和(或)内部层。
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