OptimalStrongConvergenceRateofSpectralGalerkin Exponential Euler Scheme for Parabolic SPDEs

We provide a new approach to strong error analysis of the spatial-spectral Galerkin and temporal exponential Euler scheme for a family of second-order parabolic stochastic partial differential equations (SPDEs) driven by multiplicative noise. Applying these results to the stochastic advection-diffusion-reactionequation with a gradient term driven by white noise indicates that this scheme achieves optimal strong conver gence order exactly 1/2 in space, which removes an infinitesimal factor in the literature, and 1/4 in time. Numerical experiments support our theoretical analysis.