In this work, a stochastic fractional advection diffusion model with multiplicative noise is studied numerically. The Galerkin finite element method in space and finite difference in time are used, where the fractional derivative is in Caputo sense. The error analysis is investigated via Galerkin finite element method. In terms of the Mittag Leffler function, the mild solution is obtained. For the error estimates, the strong convergence for the semi and fully discrete schemes are proved in a semigroup structure. Finally, two numerical examples are given to confirm the theoretical results.

中文翻译：

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时间分数随机半线性对流扩散方程的数值研究

在这项工作中，对具有乘性噪声的随机分数对流扩散模型进行了数值研究。使用Galerkin有限元空间方法和时间有限差分法，其中分数导数在Caputo意义上。通过Galerkin有限元方法研究了误差分析。就Mittag Leffler功能而言，获得了温和的溶液。对于误差估计，在半群结构中证明了半离散方案和完全离散方案的强收敛性。最后，通过两个数值例子验证了理论结果。