Energy-preserving splitting finite element method for nonlinear stochastic space-fractional wave equations with multiplicative noise

Abstract

It is well-known that numerical methods that preserve physical quantities of original system often yield physically reasonable results and possess better numerical stability in long-time simulations. In this paper, we propose a methodology of constructing efficient fully-discrete method preserving averaged energy evolution law for nonlinear stochastic space-fractional wave equations with multiplicative noise. Specifically, the space variable is firstly discretized by Galerkin finite element method, and then the splitting technique and averaged vector field method are employed for the time integration of the resulting spatial semi-discrete scheme. We prove that the proposed fully-discrete method preserves the averaged energy evolution law in the discrete level. Numerical experiments are given to verify the theoretical result.