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

by A. Jentzen and D. Salimova and T. Welti

(Report number 2017-51)

Abstract
In this paper we propose and analyze explicit space-time discrete numerical approximations for additive space-time white noise driven stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities such as the stochastic Burgers equation with space-time white noise. The main result of this paper proves that the proposed explicit space-time discrete approximation method converges strongly to the solution process of the stochastic Burgers equation with space-time white noise. To the best of our knowledge, the main result of this work is the first result in the literature which establishes strong convergence for a space-time discrete approximation method in the case of the stochastic Burgers equations with space-time white noise.

Keywords:

@Techreport{JSW17_747,
  author = {A. Jentzen and D. Salimova and T. Welti},
  title = {Strong convergence for explicit space-time discrete numerical approximation methods for stochastic Burgers equations},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2017-51},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2017/2017-51.pdf },
  year = {2017}
}

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