The discontinuous Galerkin (DG) method provides a robust and flexible technique for the time integration of fractional diffusion problems. However, a practical implementation uses coefficients defined by integrals that are not easily evaluated. We describe specialized quadrature techniques that efficiently maintain the overall accuracy of the DG method. In addition, we observe in numerical experiments that known superconvergence properties of DG time stepping for classical diffusion problems carry over in a modified form to the fractional-order setting.

中文翻译：

---

分数扩散问题的高阶、不连续伽辽金时间步的实现

不连续的伽辽金 (危险品) 方法为分数扩散问题的时间积分提供了一种稳健且灵活的技术。然而，实际的实现使用由不易评估的积分定义的系数。我们描述了专门的正交技术，可以有效地保持整体精度危险品方法。此外，我们在数值实验中观察到已知的超收敛特性危险品经典扩散问题的时间步长以改进的形式延续到分数阶设置。