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The main result of this article establishes strong convergence rates on thewhole probability space for explicit space-time discrete numericalapproximations for a class of stochastic evolution equations with possiblynon-globally monotone coefficients such as stochastic Burgers equations withadditive trace-class noise. The key idea in the proof of our main result is (i)to bring the classical Alekseev-Gr\"obner formula from deterministic analysisinto play and (ii) to employ uniform exponential moment estimates for thenumerical approximations.

Strong convergence rates on the whole probability space for space-time discrete numerical approximation schemes for stochastic Burgers equations