We present an error analysis for the discontinuous Galerkin method applied to the discrete-ordinate discretization of the steady-state radiative transfer equation. Under some mild assumptions, we show that the DG method converges uniformly with respect to a scaling parameter $\varepsilon$ which characterizes the strength of scattering in the system. However, the rate is not optimal and can be polluted by the presence of boundary layers. In one-dimensional slab geometries, we demonstrate optimal convergence when boundary layers are not present and analyze a simple strategy for balance interior and boundary layer errors. Some numerical tests are also provided in this reduced setting.

中文翻译：

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求解具有各向同性散射核的尺度离散纵坐标辐射传递方程的逆风不连续伽辽金方法的均匀收敛

我们对应用于稳态辐射传递方程的离散纵坐标离散化的不连续 Galerkin 方法进行了误差分析。在一些温和的假设下，我们表明 DG 方法相对于表征系统中散射强度的缩放参数 $\varepsilon$ 均匀收敛。但是，该速率不是最佳的，并且可能因边界层的存在而受到污染。在一维平板几何中，当边界层不存在时，我们展示了最佳收敛性，并分析了平衡内部和边界层误差的简单策略。在这种简化的设置中还提供了一些数值测试。