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We study the numerical approximation of stochastic evolution equations with amonotone drift driven by an infinite-dimensional Wiener process. To discretizethe equation, we combine a drift-implicit two-step BDF method for the temporaldiscretization with an abstract Galerkin method for the spatial discretization.After proving well-posedness of the BDF2-Maruyama scheme, we establish aconvergence rate of the strong error for equations under suitable Lipschitzconditions. We illustrate our theoretical results through various numericalexperiments and compare the performance of the BDF2-Maruyama scheme to thebackward Euler--Maruyama scheme.

The BDF2-Maruyama Scheme for Stochastic Evolution Equations with Monotone Drift