Stability and Optimal Error Estimates Analysis of an LDG Method for the Stochastic Nonlinear KdV Equation

To address the computational challenges of stochastic nonlinear partial differential equations with high-order derivatives, a local discontinuous Galerkin method is proposed for the stochastic KdV equation. The method is proven to be £²-stable and to attain optimal error estimates of order n +1 measured in the mean-square norm when degree-n polynomials are used. Temporal integration of the spatial semi-discrete stochastic system in the numerical experiments is carried out by using the implicit midpoint method. The simulation results verify the method’s accuracy and its consistency with the theoretical analysis.