  The main result of this article establishes strong convergence rates on the
whole probability space for explicit space-time discrete numerical
approximations for a class of stochastic evolution equations with possibly
non-globally monotone coefficients such as stochastic Burgers equations with
additive 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 analysis
into play and (ii) to employ uniform exponential moment estimates for the
numerical approximations.
