A linearized decoupled fully discrete scheme is developed and investigated for the coupled nonlinear semiconductor device problem with low order nonconforming EQ1rot element. Then, by use of its special property: the consistency error in the broken H1-norm can reach to second order when the exact solutions belong to H3(Ω), just one order higher than its interpolation error, together with some proper approaches such as the discrete derivative transfer trick, difference quotient between two adjacent time levels, mathematics induction method and so on, the difficulty caused by the nonlinearity is ingeniously coped with, and the superclose estimates about the related variables are derived rigorously. In addition, the satisfactory global superconvergence results are obtained through the interpolation postprocessing approach. Finally, a numerical example is presented to validate the theoretical analysis and the good performance of the proposed method.

中文翻译：

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耦合非线性半导体器件问题的低阶非共形有限元方法的超收敛分析


针对具有低阶非一致性 EQ1rot 元件的耦合非线性半导体器件问题，开发并研究了一种线性化解耦全离散方案。然后，利用其特殊性质：当精确解属于 H3（Ω） 时，破损的 H1 范数中的一致性误差可以达到二阶，仅比其插值误差高一个阶，再加上一些合适的方法，如离散导数传递技巧、相邻两个时间水平之间的差商、数学归纳法等， 巧妙地应对了非线性带来的困难，并严格推导了有关相关变量的超接近估计。此外，通过插值后处理方法获得了令人满意的全局超收敛结果。最后，通过数值算例验证了理论分析和所提方法的良好性能。