In this paper, we present novel cell-centered finite element methods for the convection-dominated convection–diffusion problems on the general meshes. The proposed schemes can be constructed from a general mesh by building with a dual mesh and its triangular sub-mesh. Moreover, the schemes are based on piecewise linear functions combined with two upwind techniques on the dual sub-mesh in order to stabilize the numerical solutions and eliminate the spurious oscillations. Through numerical results, two methods are shown to be effective in terms of accuracy, stability and computational cost.

中文翻译：

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一般网格上对流扩散方程的一种新的以单元为中心的迎风类型方法

在本文中，我们提出了新的以单元为中心的有限元方法，用于解决一般网格上的对流主导的对流扩散问题。所提出的方案可以通过使用双网格及其三角形子网格从一般网格构建。此外，该方案基于分段线性函数，结合双子网格上的两种迎风技术，以稳定数值解并消除寄生振荡。通过数值结果，两种方法被证明在准确性、稳定性和计算成本方面是有效的。