Xiaobing Feng, Yukun Li, Yujian Lin, Fully discrete finite element methods for nonlinear stochastic elastic wave equations with multiplicative noise, Vol. 2022 (2022), Article ID 29, pp. 1-38

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DOI: 10.23952/cot.2022.29

Received September 12, 2021; Accepted October 3, 2022; Published December 20, 2022

Abstract. This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise. A detailed analysis of the properties of the weak solution is carried out and a fully discrete finite element method is proposed. Strong convergence in the energy norm with rate $O(k+h^r)$ is proved, where $k$ and $h$ denote respectively the temporal and spatial mesh sizes, and $r(\geq 1)$ is the order of the finite element. Numerical experiments are provided to test the efficiency of proposed numerical methods and to validate the theoretical error estimate results.

How to Cite this Article:
X. Feng, Y. Li, Y. Lin, Fully discrete finite element methods for nonlinear stochastic elastic wave equations with multiplicative noise, Commun. Optim. Theory 2022 (2022) 29.