In this paper, we consider superconvergence error estimates of finite element method approximation of Caputo’s time fractional reaction–subdiffusion equations under nonuniform time meshes. For the standard Galerkin method we see that the optimal order error estimate of temporal direction cannot be derived from the weak formulation of the problem. We establish a time-space error splitting argument, which are called the temporal error and the spatial error, respectively. The temporal error is proved skillfully based on an improved discrete Grönwall inequality. We obtain the sharp temporal \(H^1\)-norm error estimates with respect to the convergence order of the approximate solution and \(H^1\)-norm superclose results are given in details. Furthermore, by virtue of the interpolated postprocessing techniques, the global \(H^1\)-norm superconvergence results are presented. Finally, we present some numerical results that give insight into the reliability of the theoretical analysis.

在本文中，我们考虑了非均匀时间网格下Caputo时间分数反应-扩散方程的有限元方法逼近的超收敛误差估计。对于标准的Galerkin方法，我们看到时间方向的最佳顺序误差估计不能从问题的弱公式中得出。我们建立一个时空误差分裂参数，分别称为时间误差和空间误差。基于改进的离散Grönwall不等式，巧妙地证明了时间误差。关于近似解和\（H ^ 1 \）的收敛顺序，我们获得了尖锐的临时\（H ^ 1 \）-范数误差估计。-norm superclose结果将详细给出。此外，借助内插后处理技术，给出了全局\（H ^ 1 \）-范数超收敛结果。最后，我们提出一些数值结果，以深入了解理论分析的可靠性。