论文标题
随机Maxwell方程的沿形数值近似值
Ergodic numerical approximations for stochastic Maxwell equations
论文作者
论文摘要
在本文中，我们提出了一种新型的数值近似值来继承随机的麦克斯韦方程的奇迹性。证明恐怖性的关键在于数值解决方案相对于时间的统一规律性估计，这是通过分析一些重要的物理量来确定的。 By introducing an auxiliary process, we show that the mean-square convergence order of the ergodic discontinuous Galerkin full discretization is $\frac{1}{2}$ in the temporal direction and $\frac{1}{2}$ in the spatial direction, which provides the convergence order of the numerical invariant measure to the exact one in $L^2$-Wasserstein 距离。
In this paper, we propose a novel kind of numerical approximations to inherit the ergodicity of stochastic Maxwell equations. The key to proving the ergodicity lies in the uniform regularity estimates of the numerical solutions with respect to time, which are established by analyzing some important physical quantities. By introducing an auxiliary process, we show that the mean-square convergence order of the ergodic discontinuous Galerkin full discretization is $\frac{1}{2}$ in the temporal direction and $\frac{1}{2}$ in the spatial direction, which provides the convergence order of the numerical invariant measure to the exact one in $L^2$-Wasserstein distance.
