In this paper, we analyze the supercloseness result of nonsymmetric interior penalty Galerkin (NIPG) method on Shishkin mesh for a singularly perturbed convection diffusion problem. According to the characteristics of the solution and the scheme, a new analysis is proposed. More specifically, Gau{\ss} Lobatto interpolation and Gau{\ss} Radau interpolation are introduced inside and outside the layer, respectively. By selecting special penalty parameters at different mesh points, we further establish supercloseness of almost k + 1 order under the energy norm. Here k is the order of piecewise polynomials. Then, a simple post processing operator is constructed. In particular, a new analysis is proposed for the stability analysis of this operator. On the basis of that, we prove that the corresponding post-processing can make the numerical solution achieve higher accuracy. Finally, superconvergence can be derived under the discrete energy norm. These theoretical conclusions can be verified numerically.

翻译：在本文中, 我们分析在希什金网格中, 使用非对称内部惩罚Galerkin( NIPG) 方法的超近距离结果, 是一个特别受扰动的对流扩散问题。 根据解决方案和计划的特点, 提议进行新的分析。 更具体地说, 分别在该层内外引入了Lobatto 内插和 Gauss} Radau 内插。 通过在不同网格点选择特殊惩罚参数, 我们进一步在能源规范下建立几乎 k+ 1 命令的超近距离。 这里 k 是一个小圆形的多面体顺序 。 然后, 构建了一个简单的后端处理操作器。 特别是, 为该操作器的稳定性分析建议了新的分析 。 在此基础上, 我们证明相应的后处理可以提高数字解决方案的精确度。 最后, 可以在离散能源规范下生成超级相容值。 这些理论结论可以被数校准 。