We consider a singularly perturbed convection-diffusion boundary value problem whose solution contains exponential and characteristic boundary layers. The problem is numerically solved by the FEM and SDFEM method with bilinear elements on a graded mesh. For the FEM we prove almost uniform convergence and superconvergence. The use of a graded mesh allows for the SDFEM to yield almost uniform estimates in the SD norm, which is not possible for Shishkin type meshes. Numerical results are presented to support theoretical bounds.

中文翻译：

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具有特征层问题的渐变网格上的FEM和SDFEM超收敛分析

我们考虑奇异摄动对流扩散边界值问题，其解包含指数边界层和特征边界层。通过在渐变网格上使用双线性元素的FEM和SDFEM方法以数值方式解决了该问题。对于FEM，我们证明了几乎一致的收敛和超收敛。使用渐变网格可以使SDFEM在SD范本中产生几乎统一的估计，这对于Shishkin类型的网格是不可能的。给出数值结果以支持理论范围。