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

2024/01/18 by Zhou, Qin, Li, Binjie
#60H15 #60H35 #65M60 #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR)

paper · doi:10.48550/arxiv.2401.09834

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 (L²)-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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