Convergent numerical approximation of the stochastic total variation flow with linear multiplicative noise: the higher dimensional case

TL;DR

This paper extends the convergence analysis of a finite element scheme for the stochastic total variation flow with linear multiplicative noise to higher spatial dimensions, overcoming previous dimensional limitations.

Contribution

It generalizes the convergence proof of the numerical scheme for STVF with noise from one to higher dimensions, addressing a key theoretical gap.

Findings

Convergence proof successfully extended to higher dimensions.

Numerical scheme remains stable and accurate in multiple dimensions.

Addresses a significant challenge in stochastic PDE approximation.

Abstract

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.