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:在本文中,我们首次研究非对称内部惩罚Galerkin(NIPG)方法在Bakhvalov型网状网格上的趋同性。 为此,我们设计了一种新的复合内插法,解决了分析Bakhvalov型网格的内在困难。更具体地说,Gauss Radau 内插法和Gaus Lobatto内插法分别用于该层内外。在此基础上,通过在不同网格点选择惩罚参数的具体值,我们得出了1美元+1/2美元超接近值,并证明了在能源规范中最佳秩序的趋同性。理论结论与数字结果是一致的。</s>