论文标题
P-Robust多边形不连续的Galerkin方法，具有负稳定
A p-robust polygonal discontinuous Galerkin method with minus one stabilization
论文作者
论文摘要
我们引入了针对多边形网格上泊松问题的不连续的盖尔金方法的新稳定化，该方法诱导多项式近似程度$ p $中的最佳收敛速率。在[S. Bertoluzza和D. Prada，一种多边形的盖尔金方法，具有减去一个稳定的esaim Math。 mod。 numer。肛门。 （doi：10.1051/m2an/2020059）]，通过在每个网格元素$ k $中惩罚稳定，这是$ h^1（k）$的二重要的残留物。通过引入新的辅助空间来实现该负标准。我们进行了$ p $ - 说明稳定性和错误分析，证明了$ p $ - 整体方法的努力。理论发现在一系列数值实验中得到了证明。
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 $p$. In the setting of [S. Bertoluzza and D. Prada, A polygonal discontinuous Galerkin method with minus one stabilization, ESAIM Math. Mod. Numer. Anal. (DOI: 10.1051/m2an/2020059)], the stabilization is obtained by penalizing, in each mesh element $K$, a residual in the norm of the dual of $H^1(K)$. 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.
