In this article, we study the convergence properties of the streamline-diffusion finite element method (SDFEM) for singularly perturbed 1D parabolic convection–diffusion initial-boundary-value problems. To discretize the spatial domain, we use a layer-adaptive nonuniform grids obtained through the equidistribution principle, whereas uniform grid is used in the time direction. Here, we use the backward-Euler method to discretize the temporal derivative and the SDFEM scheme for the spatial derivatives. The proposed method is uniformly convergent with first-order in time and second-order in space.

中文翻译：

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SDFEM用于等分分布网格上的奇摄动抛物线初边值问题

在本文中，我们研究了奇异摄动一维抛物线对流扩散初始边界值问题的流线扩散有限元方法（SDFEM）的收敛性质。为了使空间域离散化，我们使用通过等分分布原理获得的层自适应非均匀网格，而在时间方向上使用均匀网格。在这里，我们使用后向欧拉方法离散化时间导数和空间导数的SDFEM方案。所提出的方法在时间上是一阶的，在空间上是二阶的。