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 discretization, we employ quadtree-like grids, which allow for local refinement in phase-space, and we show exemplary that adaptive methods can efficiently approximate discontinuous solutions.

翻译：我们得出并分析一个对称的内置惩罚不连续加勒金计划,以近似辐射传输方程式的二阶形式在板块几何学中。 使用适当的微量 Lemmas, 分析可以作为更标准的椭圆问题来进行。 辅助示例也用数字来显示这种方法的准确性和稳定性。 对于分解, 我们使用四边形的网格, 以便局部改进相位空间, 我们展示了适应方法能够有效地近似不连续解决方案的典范。