In this work, the numerical approximation of the time-fractional mobile/immobile transport equation is considered. We investigate the solution regularity for two types of the initial data regularities. By applying the continuous piecewise linear finite elements in space, we obtain the spatial semidiscrete Galerkin scheme and derive its error estimates. We then propose two finite element schemes for the equation by employing convolution quadrature based on the backward Euler and the second-order backward difference methods. The corresponding error estimates for the two schemes are also given. Numerical examples of the two-dimensional problems are shown to confirm the convergence theory results.

在这项工作中，考虑了时间分数移动/不动传输方程的数值近似。我们调查两种初始数据规律性的解决方案规律性。通过在空间中应用连续的分段线性有限元，我们获得了空间半离散Galerkin方案并推导了其误差估计。然后，通过基于后向欧拉和二阶后向差分方法的卷积求积法，为方程式提出了两种有限元方案。还给出了两种方案的相应误差估计。给出了二维问题的数值例子，以证实收敛理论的结果。