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

TL;DR

This paper introduces and proves the strong convergence of an explicit space-time discretization method for stochastic Burgers equations driven by space-time white noise, a novel result in the field of SPDE numerical analysis.

Contribution

It is the first to establish strong convergence of a space-time discrete approximation for stochastic Burgers equations with white noise.

Findings

Proposed explicit discretization converges strongly to the solution.

First proof of strong convergence for this class of SPDEs.

Advances numerical methods for stochastic PDEs with non-globally monotone nonlinearities.

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.