In this paper, we focus on constructing numerical schemes preserving the averaged energy evolution law for nonlinear stochastic wave equations driven by multiplicative noise. We first apply the compact finite difference method and the interior penalty discontinuous Galerkin finite element method to discretize space variable and present two semi-discrete schemes, respectively. Then we make use of the discrete gradient method and the Padé approximation to propose efficient fully-discrete schemes. These semi-discrete and fully-discrete schemes are proved to preserve the discrete averaged energy evolution law. In particular, we also prove that the proposed fully-discrete schemes exactly inherit the energy evolution law almost surely if the considered model is driven by additive noise. Numerical experiments are given to confirm theoretical findings.

　　Publication: 

　　Journal of Computational Physics, Volume 451, 15 February 2022 

　　Author: 

　　Jialin Hong 

　　Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 

　　School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China 

　　E-mail: hjl@lsec.cc.ac.cn  

　　Baohui Hou 

　　Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 

　　E-mail: houbaohui@lsec.cc.ac.cn  

　　Liying Sun 

　　Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 

　　E-mail: liyingsun@lsec.cc.ac.cn