In this paper, we study the convergence of the nonsymmetric interior penalty Galerkin (NIPG) method on a Bakhvalov-type mesh for the first time. For this purpose, a new composite interpolation is designed, which solves the inherent difficulty of analysis on Bakhvalov-type meshes. More specifically, Gauss Radau interpolation and Gauss Lobatto interpolation are used outside and inside the layer, respectively. On the basis of that, by choosing the specific values of the penalty parameters at different mesh points, we derive the supercloseness of $k+1/2$th order ($k\ge 1$), and prove the convergence of optimal order in an energy norm. The theoretical conclusion is consistent with the numerical results.

翻译：本文首次研究了Bakhvalov型网格上非对称内罚Galerkin(NIPG)方法的收敛性。为此，我们设计了一种新的复合插值方法，解决了Bakhvalov型网格分析中的固有困难。具体而言，在层外和层内分别采用Gauss Radau插值和Gauss Lobatto插值。在此基础上，通过在不同网格点选取特定的罚参数值，我们推导出了$k+1/2$阶（$k\ge 1$）的超逼近性，并证明了能量范数下的最优收敛阶。理论结论与数值结果一致。