In this paper, we present a unified analysis of the superconvergence property for a large class of mixed discontinuous Galerkin methods. This analysis applies to both the Poisson equation and linear elasticity problems with symmetric stress formulations. Based on this result, some locally postprocess schemes are employed to improve the accuracy of displacement by order \(\min (k+1, 2)\) if polynomials of degree k are employed for displacement. Some numerical experiments are carried out to validate the theoretical results.

中文翻译：

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椭圆边值问题的不连续伽辽金方法的超收敛

在本文中，我们对一大类混合不连续伽辽金方法的超收敛特性进行了统一分析。此分析适用于具有对称应力公式的 Poisson 方程和线性弹性问题。基于此结果，如果采用k次多项式进行位移，则采用一些局部后处理方案来提高按\(\min (k+1, 2)\)阶位移的精度。进行了一些数值实验来验证理论结果。