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

10/02/2022

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by   Xiaobing Feng, et al.

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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(≥ 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.