Numerical Simulations for Parabolic Stochastic Equations Using a Structure-Preserving Local Discontinuous Galerkin Method

In this paper, a structure-preserving local discontinuous Galerkin (LDG) method is proposed for parabolic stochastic partial differential equations with periodic boundary conditions and multiplicative noise. It is proven that under certain conditions, this numerical method is stable in the L2 sense and can preserve energy conservation. The optimal spatial error estimate in the mean square sense can reach n+1 if the degree of the polynomial is n. The correctness of the theoretical results is verified through numerical examples.