Fully discrete finite element methods for nonlinear stochastic elastic wave equations with multiplicative noise

2022/10/02 by Xiaobing Feng, Yukun Li, Feng, Xiaobing +3
Economics, Econometrics and Finance · #65C30 #65M12 #65M15 #65M60 #FOS: Mathematics #Numerical Analysis (math.NA) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2210.00592

openalex publication_date 2022/10/02 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

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 \calO(k+h^r) is proved, where k and h denote respectively the temporal and spatial mesh sizes, and r(≥ 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.

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