Abstract
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.
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