In this paper, the discontinuous Galerkin method (DGM) of nonconforming Wilson element is studied for the semi-linear parabolic problem. The global superconvergence with respect to the mesh size are derived in the modified $H^1$-norm for the semi-discrete scheme and two fully discrete schemes, in which the usual extrapolation and interpolation post-processing approaches are not involved, and the error estimates are one order higher than that of the traditional Galerkin finite element method (FEM). Therefore, the corresponding results in the existing literature are improved. Finally, some numerical results are provided to confirm the theoretical analysis.

中文翻译：

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半线性抛物线问题非相容威尔逊有限元超收敛分析的新方法

本文针对半线性抛物线问题，研究了非协调威尔逊单元的不连续伽勒金方法（DGM）。相对于网格尺寸的全局超收敛性是在修改后的结果中得出的$H^{\mathrm{1个}}$-标准适用于半离散方案和两个完全离散方案，其中不包括通常的外推法和内插法后处理方法，并且误差估计比传统的Galerkin有限元方法（FEM）高一阶。因此，现有文献中的相应结果得到了改善。最后，提供一些数值结果以证实理论分析。