This paper is devoted to the study of nonlinear Ginzburg-Landau equation (GLE) with the nonconforming modified quasi-Wilson quadrilateral finite element. Based on the special property of this element, that is its consistency error can reach order in the broken -norm when the exact solution belongs to , and by use of the interpolated postprocessing technique, the superclose and superconvergence estimates are obtained for the semi-discrete scheme with order , the Backward-Euler (B-E) fully-discrete scheme with order , and the Crank-Nicolson (C-N) fully-discrete scheme with order , respectively. In addition, a numerical example is provided to verify the theoretical analysis. Here is the mesh size and △ is the time step.

中文翻译：

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非线性Ginzburg-Landau方程的非相容四边形有限元分析


本文致力于研究非协调修正拟Wilson四边形有限元的非线性Ginzburg-Landau方程（GLE）。基于该单元的特殊性质，即当精确解属于 时，其一致性误差可达到破范量级，利用插值后处理技术，获得了半离散模型的超接近和超收敛估计。分别为阶数为 的方案、阶数为 的后向欧拉 (BE) 全离散格式和阶数为 的 Crank-Nicolson (CN) 全离散格式。此外，还提供了数值算例来验证理论分析。这里是网格尺寸，△是时间步长。