We study the convergence of the discontinuous Galerkin (DG) method applied to the advection-reaction equation on meshes with reentrant faces. On such meshes, the upwind numerical flux is not smooth, and so the numerical integration of the resulting face terms can only be expected to be first-order accurate. Despite this inexact integration, we prove that the DG method converges with order $\mathcal{O}(h^{p+1/2})$, which is the same rate as in the case of exact integration. Consequently, specialized quadrature rules that accurately integrate the non-smooth numerical fluxes are not required for high-order accuracy. These results are numerically corroborated on examples of linear advection and discrete ordinates transport equations.
翻译：我们研究对正反动反应方程式使用的不连续的Galerkin(DG)方法的趋同性。 在这种模子上,上风数字通量不平滑,因此由此得出的表面条件的数值整合只能预计为第一级准确。尽管这种不精确的整合,但我们证明DG方法与美元对冲/O}(h ⁇ p+1/2})($mathcal{O}(h ⁇ p+1/2)($)相近,这与精确的整合情况相同。 因此,在高序精度中,不需要精确结合非移动数字通量的专门等式规则。这些结果在线性对冲和离散坐标运方程式的例子中得到了数字上的证实。
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