Energy-preserving fully-discrete schemes for nonlinear stochastic wave equations with multiplicative noise

被引：0

作者：

Hong, Jialin ^{[1
,2
]}

Hou, Baohui ^{[1
]}

Sun, Liying ^{[1
]}

机构：

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

[2] School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing,100049, China

来源：

Journal of Computational Physics | 2022年 / 451卷

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

Additive noise - Finite element method - Galerkin methods - Gradient methods - Nonlinear equations - Phase noise - Stochastic systems - Wave equations;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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. © 2021 Elsevier Inc.

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