In this paper, a mixed finite element method is applied in spatial directions while keeping time variable continuous to a class of time-fractional diffusion problems with time-dependent coefficients on a bounded convex polygonal domain. Based on an energy argument combined with a repeated application of an integral operator, optimal error estimates, which are optimal with respect to both approximation properties and regularity results, are derived for the semidiscrete problem with smooth as well as nonsmooth initial data. Specially, a priori error bounds for both primary and secondary variables in \(L^2\)-norm are established. Since the comparison between Fortin projection and the mixed Galerkin approximation of the secondary variable yields an improved rate of convergence, therefore, as a by-product, we derive \(L^p\)-estimates for the error in primary variable. Finally, some numerical experiments are conducted to confirm our theoretical findings.

在本文中，在空间方向上应用混合有限元方法，同时将时间变量连续化为有界凸多边形域上一类具有时间相关系数的时间分数阶扩散问题。基于能量论证并重复应用积分算子，针对具有离散和非平稳初始数据的半离散问题，得出了最佳误差估计，该误差估计在近似性质和规则性结果方面均最佳。特别地，\（L ^ 2 \）中主要变量和次要变量的先验误差范围-规范建立。由于在Fortin投影和次级变量的混合Galerkin逼近之间进行比较，可以提高收敛速度，因此，作为副产品，我们得出\（L ^ p \）-初级变量的误差估计。最后，进行了一些数值实验以证实我们的理论发现。