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We establish a unconditional and optimal strong convergence rate ofWong--Zakai type approximations in Banach space norm for a parabolic stochasticpartial differential equation with monotone drift, including the stochasticAllen--Cahn equation, driven by an additive Brownian sheet. The key ingredientin the analysis is the fully use of additive nature of the noise andmonotonicity of the drift to derive a priori estimation for the solution ofthis equation, in combination with the factorization method and stochasticcalculus in martingale type 2 Banach spaces applied to deduce sharp errorestimation between the exact and approximate Ornstein--Uhlenbeck processes, inBanach space norm.

Wong--Zakai Approximations of Stochastic Allen-Cahn Equation