It is the first time for us to investigate the superconvergence of finite element method for second-degree elliptic problem with periodic boundary. Using the interpolation postprocessing technique, we obtain \(O(h^{k+1}|\ln h|^{2})\) convergence for the derivative of approximations with a \(P_{k}\) finite element method at vertex. Numerical results are used to demonstrate the effectiveness of the proposed method.

中文翻译：

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具有周期边界的二阶椭圆问题的高阶有限元方法的超收敛性

具有周期边界的二阶椭圆问题的有限元方法的超收敛性是我们的首次研究。使用内插后处理技术，我们使用\（P_ {k} \）有限元方法获得近似导数的\（O（h ^ {k + 1} | \ ln h | ^ {2}）\）收敛在顶点。数值结果证明了该方法的有效性。