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arXiv · 2303.13125

Finite Volume Approximations for Non-Linear Parabolic Problems with Stochastic Forcing

Caroline Bauzet·Flore Nabet·Kerstin Schmitz·Aleksandra Zimmermann
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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.

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Caroline Bauzet, Flore Nabet, Kerstin Schmitz, Aleksandra Zimmermann. 2023-03-23. Finite Volume Approximations for Non-Linear Parabolic Problems with Stochastic Forcing. https://arxiv.org/abs/2303.13125

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