In this paper, we study the solute transport in heterogeneous media described by the time-fractional mobile/immobile advection diffusion model, where the integer and the fractional time derivatives are employed to characterize the movement of the particles in the mobile and immobile zone, respectively. We propose a fully discrete characteristic finite element scheme for the model, in which the modified method of characteristics is applied to handle the domination of advection. The optimal L² error estimate is derived with first-order accuracy in time and second-order accuracy in space. Several practical numerical experiments are presented to validate the effectiveness and accuracy of the proposed method.

在本文中，我们研究了时分移动/不动平流扩散模型所描述的非均质介质中的溶质运移，其中整数和分数时间导数分别用于表征粒子在移动区和固定区内的运动。 。我们为模型提出了一种完全离散的特征有限元方案，其中采用了改进的特征方法来处理对流的控制。最佳的L ²误差估计是在时间上具有一阶精度而在空间上具有二阶精度。提出了一些实用的数值实验，以验证该方法的有效性和准确性。