Convergence of a spatial semidiscretization for a three-dimensional stochastic Allen-Cahn equation with multiplicative noise
Numerical Analysis
2025-07-25 v8 Numerical Analysis
Probability
Abstract
This paper studies the convergence of a spatial semidiscretization of a three-dimensional stochastic Allen-Cahn equation with multiplicative noise. For non-smooth initial data, the regularity of the mild solution is investigated, and an error estimate is derived within the spatial (L^2)-norm setting. In the case of smooth initial data, two error estimates are established within the framework of general spatial (L^q)-norms.
Keywords
Cite
@article{arxiv.2401.09834,
title = {Convergence of a spatial semidiscretization for a three-dimensional stochastic Allen-Cahn equation with multiplicative noise},
author = {Qin Zhou and Binjie Li},
journal= {arXiv preprint arXiv:2401.09834},
year = {2025}
}