A structure-preserving local discontinuous Galerkin method for the stochastic KdV equation

Abstract

This paper proposes a local discontinuous Galerkin (LDG) method for the stochastic Korteweg-de Vries (KdV) equation with multi-dimensional multiplicative noise. In the mean square sense, we show that the numerical method is $L^2$ stable and it preserves energy conservation and energy dissipation. If the degree of the polynomial is n, the optimal error estimate in the mean square sense can reach as $n+1$. Finally, structure-preserving and convergence are verified by numerical experiments.