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.
翻译:我们考虑的是“STVF”与“cite{our_paper}”中先前提议的线性多倍噪声的完全离散的有限元素总流方程近似值。由于缺乏在较高空间层面更强的先验估计的离散对应值,对数字法最初的趋同分析仅限于一个空间层面,参见“cite{stvf_erratum}”。本文将趋同证据概括为更高层面。