论文标题
具有乘法噪声的非线性随机弹性波方程的完全离散的有限元方法
Fully discrete finite element methods for nonlinear stochastic elastic wave equations with multiplicative noise
论文作者
论文摘要
本文涉及完全分散的有限元方法，用于近似具有乘法噪声的非线性随机弹性波方程的变异溶液。对弱解的性质进行了详细分析，并提出了完全离散的有限元方法。证明了$ \ cal {o}（k+h^r）$的能源规范的强收敛，其中$ k $和$ h $分别表示时间和空间网状尺寸，而$ r（\ geq 1）$是有限元的顺序。提供数值实验来测试提出的数值方法的效率并验证理论误差估计结果。
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 $\cal{O}(k+h^r)$ 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.
