As a popular stabilization technique, the nonsymmetric interior penalty Galerkin (NIPG) method has significant application value in computational fluid dynamics. In this paper, we study the NIPG method for a typical two-dimensional singularly perturbed convection diffusion problem on a Shishkin mesh. According to the characteristics of the solution, the mesh and numerical scheme, a new composite interpolation is introduced. In fact, this interpolation is composed of a vertices-edges-element interpolation within the layer and a local $L^{2}$-projection outside the layer. On the basis of that, by selecting penalty parameters on different types of interelement edges, we further obtain the supercloseness of almost $k+\frac{1}{2}$ order in an energy norm. Here $k$ is the degree of piecewise polynomials. Numerical tests support our theoretical conclusion.

翻译：作为流行的稳定化技术,非对称内部惩罚Galerkin(NIPG)方法在计算流体动态中具有相当大的应用价值。 在本文中,我们研究了用于Shishkin网状中典型的二维单扰动对流扩散问题的NIPG方法。根据解决方案的特征,网格和数字方法,引入了新的复合内插法。事实上,这种内插法由层内脊椎-边缘-内元素的内插法和层外本地的$L<unk> 2}美元投射法组成。在此基础上,我们通过选择不同类型间缘边缘的处罚参数,在能源规范中进一步获得了近乎 $kfrac{1<unk> 2}的超近距离值。这里的美元是小巧的多元度。 数字测试支持了我们的理论结论 。</s>