论文标题
平面空间不连续的Galerkin近似，用于平板几何形状中的辐射传递方程
A phase-space discontinuous Galerkin approximation for the radiative transfer equation in slab geometry
论文作者
论文摘要
我们得出并分析了对称的内部惩罚不连续的盖尔金方案，以在平板几何形状中辐射传递方程的二阶形式的近似。使用适当的痕量引理，可以针对更标准的椭圆问题进行分析。支持示例表明，对于不同的多项式程度，该方法的准确性和稳定性也在数值上。为了离散化，我们采用了四轮元网格，可以在相位空间中进行局部细化，并且表明自适应方法可以有效地近似不连续的解决方案。我们根据局部平均研究研究了层次误差估计器和误差估计器的行为。
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.
