Full discretization of the stochastic Burgers equation with correlated noise

The main purpose of this paper is to investigate the spectral Galerkin method for spatial discretization. We combine it with the method introduced by Jentzen et al. (2011, Efficient simulation of nonlinear parabolic SPDEs with additive noise. Ann. Appl. Probab., 21, 908–950) for temporal discretization of stochastic partial differential equations and study pathwise convergence. We consider the case of coloured noise, instead of the usual space-time white noise that was used before for the spatial discretization. The rate of convergence in uniform topology is estimated for the stochastic Burgers' equation. Numerical examples illustrate the estimated convergence rate.