论文标题
随机总变化流动与线性乘法噪声的收敛数值近似：较高的尺寸情况
Convergent numerical approximation of the stochastic total variation flow with linear multiplicative noise: the higher dimensional case
论文作者
论文摘要
我们考虑使用线性乘法噪声的随机总变化流动方程（STVF）的完全离散的有限元近似，该噪声先前是在\ cite {our_paper}中提出的。由于缺乏较高空间维度的先验估计值的离散对应物，因此数值方案的原始收敛分析仅限于一个空间维度，请参见。 \ cite {stvf_erratum}。在本文中，我们将收敛证明推广到更高的维度。
We consider fully discrete finite element approximation of the stochastic total variation flow equation (STVF) with linear multiplicative noise which was previously proposed in \cite{our_paper}. Due to lack of a discrete counterpart of stronger a priori estimates in higher spatial dimensions the original convergence analysis of the numerical scheme was limited to one spatial dimension, cf. \cite{stvf_erratum}. In this paper we generalize the convergence proof to higher dimensions.
