In this paper, we introduce a new stabilization for discontinuous Galerkin methods for the Poisson problem on polygonal meshes, which induces optimal convergence rates in the polynomial approximation degree p. The stabilization is obtained by penalizing, in each mesh element K, a residual in the norm of the dual of H1(K). This negative norm is algebraically realized via the introduction of new auxiliary spaces. We carry out a p-explicit stability and error analysis, proving p-robustness of the overall method. The theoretical findings are demonstrated in a series of numerical experiments.

中文翻译：

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一种具有负一稳定性的 p-robust 多边形间断 Galerkin 方法

在本文中，我们为多边形网格上的 Poisson 问题引入了一种新的非连续 Galerkin 方法的稳定性，它在多项式逼近度中引入了最优收敛速度p. 通过在每个网格元素中进行惩罚来获得稳定性ķ，对偶范数中的残差H1(ķ). 这种负范数是通过引入新的辅助空间在代数上实现的。我们进行了一次p-明确的稳定性和误差分析，证明p- 整体方法的稳健性。理论发现在一系列数值实验中得到证明。