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arXiv · 2401.09834

Convergence of a spatial semidiscretization for a three-dimensional stochastic Allen-Cahn equation with multiplicative noise

Qin Zhou·Binjie Li
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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.

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Qin Zhou, Binjie Li. 2024-01-18. Convergence of a spatial semidiscretization for a three-dimensional stochastic Allen-Cahn equation with multiplicative noise. https://arxiv.org/abs/2401.09834

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