Fractional Klein-Kramers equation can well describe subdiffusion in phase space. In this paper, we develop the fully discrete scheme for fractional Klein-Kramers equation based on the backward Euler convolution quadrature and local discontinuous Galerkin methods. Thanks to the obtained sharp regularity estimates in temporal and spatial directions after overcoming the hypocoercivity of the operator, the complete error analyses of the fully discrete scheme are built. % , the main challenge of which comes from the hypocoercivity of the operator. It's worth mentioning that the convergence of the provided scheme is independent of the temporal regularity of the exact solution. Finally, numerical results are proposed to verify the correctness of the theoretical results.
翻译:分形克莱因- 克拉默斯方程式可以很好地描述相位空间的子扩散。 在本文中, 我们根据落后的欧拉革命二次曲线和局部不连续的加勒金方法, 开发了分形克莱因- 克拉默斯方程式的完全独立的方案。 由于在克服操作员的低调之后在时间和空间方向上获得了敏锐的规律性估计, 对完全独立的系统进行了完整的错误分析 。%, 其主要挑战来自操作员的低调。 值得一提的是, 所提供的方法的趋同与确切解决方案的属时规律性无关。 最后, 提出了数字结果以核实理论结果的正确性。