Abstract This paper formulates and analyzes symmetric dual-wind discontinuous Galerkin (DG) methods for second order elliptic obstacle problem. These new methods follow from the DG differential calculus framework that defines discrete differential operators to replace the continuous differential operators when discretizing a partial differential equation (PDE). We establish optimal a priori error estimates for both linear and quadratic elements provided the exact solution is sufficiently regular. These results are also shown to hold for some non-positive penalty parameters, with the emphasis on zero penalization across all interior and boundary edges. Numerical experiments are provided to validate the theoretical results and gauge the performance of the proposed methods.

中文翻译：

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障碍问题对称双风间断Galerkin逼近方法的收敛性分析

摘要 提出并分析了求解二阶椭圆障碍问题的对称双风非连续伽辽金(DG)方法。这些新方法遵循 DG 微分框架，该框架定义了离散微分算子以在离散偏微分方程 (PDE) 时替换连续微分算子。我们为线性和二次元素建立最佳先验误差估计，前提是精确解足够规则。这些结果也被证明适用于一些非正惩罚参数，重点是所有内部和边界边缘的零惩罚。提供了数值实验来验证理论结果并衡量所提出方法的性能。