We derive and analyze a symmetric interior penalty discontinuous Galerkin scheme for the approximation of the second-order form of the radiative transfer equation in slab geometry. Using appropriate trace lemmas, the analysis can be carried out as for more standard elliptic problems. Supporting examples show the accuracy and stability of the method also numerically, for different polynomial degrees. For discretization, we employ quad-tree grids, which allow for local refinement in phase-space, and we show exemplary that adaptive methods can efficiently approximate discontinuous solutions. We investigate the behavior of hierarchical error estimators and error estimators based on local averaging.

翻译：我们推导并分析了一种对称内罚间断伽辽金格式，用于逼近平板几何中二阶形式的辐射传输方程。利用适当的迹引理，该分析可按照更标准椭圆问题的思路进行。支持性算例表明该方法在不同多项式阶数下均具有数值精度和稳定性。在离散化过程中，我们采用四叉树网格以实现相空间局部细化，并通过示例展示自适应方法可高效逼近间断解。我们研究了分层误差估计器和基于局部平均的误差估计器的行为特性。