In this paper, a class of two-dimensional (2-D) time fractional reaction-diffusion equation is considered. The solution usually exhibits singularity at the initial moment and anisotropic behavior in the spatial direction. In response to these problems, we provide an effective numerical framework for analyzing the $L^2$-norm error, $H^1$-norm superclose property and $H^1$-norm global superconvergence result. This framework combines the high-precision L2-$1_{\sigma }$ scheme on non-uniform time grids and the anisotropic nonconforming quasi-Wilson finite element method (FEM) in space. Some numerical experiments are presented to illustrate our theoretical findings.

中文翻译：

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具有各向异性数据的时间分数反应-扩散问题非一致性有限元法的全局超收敛分析

在本文中，考虑了一类二维（2-D）时间分数反应-扩散方程。该解通常在初始时刻表现出奇异性和在空间方向上的各向异性行为。针对这些问题，我们提供了一个有效的数值框架来分析${\mathrm{大号}}^2$-规范错误，$H^1$-规范超关闭属性和$H^1$-norm 全局超收敛结果。该框架结合了高精度L 2-$1_{\sigma }$非均匀时间网格方案和空间中的各向异性非一致性准威尔逊有限元法（FEM）。提出了一些数值实验来说明我们的理论发现。