论文标题
关于与噪声的分数保护法的数值方案的收敛速率
On the rate of convergence of a numerical scheme for fractional conservation laws with noise
论文作者
论文摘要
我们考虑了一个由圆柱维护过程驱动的退化分数保护定律的半差异有限体积方案。利用有界变异（BV）估计值，年轻度量理论以及对经典Kruzkov理论的巧妙适应，我们提供了有关分数问题的近似解决方案收敛速率的估计。主要困难源于退化的分数操作员，并且需要与现有策略建立Kato的不平等类型。最后，作为该理论的应用，我们证明了数值收敛速率。
We consider a semi-discrete finite volume scheme for a degenerate fractional conservation laws driven by a cylindrical Wiener process. Making use of the bounded variation (BV) estimates, Young measure theory, and a clever adaptation of classical Kruzkov theory, we provide estimates on the rate of convergence for approximate solutions to fractional problems. The main difficulty stems from the degenerate fractional operator, and requires a significant departure from the existing strategy to establish Kato's type of inequality. Finally, as an application of this theory, we demonstrate numerical convergence rates.
