In this paper, based on the special property of the lowest order rectangular Raviart–Thomas element on the rectangulation and skillfully dealing with the nonlinear term, the superclose estimates for original and flux variables in $L^{\infty }\left(L^2\right)$-norm are derived firstly for the semilinear parabolic equation with backward Euler discretization in temporal direction. Then, by using a simple and efficient interpolation postprocessing approach, the global superconvergence results are obtained. Finally, a numerical experiment is provided to confirm the correctness of the theoretical analysis.

中文翻译：

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半线性抛物方程的最低阶矩形Raviart-Thomas元素的超收敛性分析

本文基于最低阶矩形Raviart–Thomas元素在矩形化上的特殊性质，并巧妙地处理非线性项，对原始和通量变量的超闭合估计 ${\mathrm{大号}}^{\infty }（{\mathrm{大号}}^2）$首先针对半线性抛物方程推导-范数，该方程在时间方向上具有反向欧拉离散。然后，通过使用简单有效的插值后处理方法，获得全局超收敛结果。最后，通过数值实验验证了理论分析的正确性。