This paper analyzes a full discretization of a three-dimensional stochastic Allen-Cahn equation with multiplicative noise. The discretization uses the Euler scheme for temporal discretization and the finite element method for spatial discretization. By deriving a stability estimate of a discrete stochastic convolution and utilizing this stability estimate along with the discrete stochastic maximal $L^p$-regularity estimate, a pathwise uniform convergence rate with the general spatial $ L^q $-norms is derived.
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