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Convergence of a spatial semidiscretization for a three-dimensional stochastic Allen-Cahn equation with multiplicative noise (2401.09834v7)

Published 18 Jan 2024 in math.NA, cs.NA, and math.PR

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 (Lq)-norms.

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