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In this paper we propose and analyze explicit space-time discrete numericalapproximations for additive space-time white noise driven stochastic partialdifferential equations (SPDEs) with non-globally monotone nonlinearities suchas the stochastic Burgers equation with space-time white noise. The main resultof this paper proves that the proposed explicit space-time discreteapproximation method converges strongly to the solution process of thestochastic Burgers equation with space-time white noise. To the best of ourknowledge, the main result of this work is the first result in the literaturewhich establishes strong convergence for a space-time discrete approximationmethod in the case of the stochastic Burgers equations with space-time whitenoise.

Strong convergence for explicit space-time discrete numerical approximation methods for stochastic Burgers equations