标题： 非光滑初始数据的反向分数阶费曼-卡克方程的误差估计 显示英文标题

标题： Error estimates for backward fractional Feynman-Kac equation with non-smooth initial data

摘要： 本文中，我们关注带有非光滑初始数据的反向分数阶Feynman-Kac方程的数值解法。 此处我们首先提供解的正则性估计。 然后我们使用向后欧拉和二阶向后差分卷积求积法来近似Riemann-Liouville分数阶本质导数，并在时间上得到一阶和二阶收敛性。 有限元方法用于离散拉普拉斯算子，并获得最优收敛率。 与之前关于反向分数阶Feynman-Kac方程的工作相比，当前离散化的主要优势是我们不需要对解在时间和空间方向上的正则性做出假设。 此外，还提供了时间半离散格式和全离散格式的误差估计。 最后，我们进行了数值实验以验证所提出算法的有效性。 显示英文摘要

摘要： In this paper, we are concerned with the numerical solution for the backward fractional Feynman-Kac equation with non-smooth initial data. Here we first provide the regularity estimate of the solution. And then we use the backward Euler and second-order backward difference convolution quadratures to approximate the Riemann-Liouville fractional substantial derivative and get the first- and second-order convergence in time. The finite element method is used to discretize the Laplace operator with the optimal convergence rates. Compared with the previous works for the backward fractional Feynman-Kac equation, the main advantage of the current discretization is that we don't need the assumption on the regularity of the solution in temporal and spatial directions. Moreover, the error estimates of the time semi-discrete schemes and the fully discrete schemes are also provided. Finally, we perform the numerical experiments to verify the effectiveness of the presented algorithms.