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.
翻译:本文涉及非线性随机弹性波波方程式的近乎离散的有限要素方法,该方法具有多倍的噪音,对弱性溶液的特性进行了详细分析,并提出了完全离散的有限要素方法。能源规范与美元/Cal{O}(k+h})(k+h ⁇ r)的汇率高度趋同,证明用美元和美元表示时间和空间网目大小,美元/Geq:1美元分别表示时间和空间网目尺寸,美元/Geq-1美元是限定要素的顺序。提供了数字实验,以测试拟议数字方法的效率,并验证理论误差估计结果。