Finite Volume Approximations for Non-Linear Parabolic Problems with Stochastic Forcing
Numerical Analysis
2023-03-24 v1 Numerical Analysis
Analysis of PDEs
Abstract
We propose a two-point flux approximation finite-volume scheme for a stochastic non-linear parabolic equation with a multiplicative noise. The time discretization is implicit except for the stochastic noise term in order to be compatible with stochastic integration in the sense of It\^{o}. We show existence and uniqueness of solutions to the scheme and the appropriate measurability for stochastic integration follows from the uniqueness of approximate solutions.
Keywords
Cite
@article{arxiv.2303.13125,
title = {Finite Volume Approximations for Non-Linear Parabolic Problems with Stochastic Forcing},
author = {Caroline Bauzet and Flore Nabet and Kerstin Schmitz and Aleksandra Zimmermann},
journal= {arXiv preprint arXiv:2303.13125},
year = {2023}
}