We propose a Discontinuous Galerkin method for the Poisson equation on polygonal tessellations in two dimensions, stabilized by penalizing, locally in each element $K$, a residual term involving the fluxes, measured in the norm of the dual of $H^1(K)$. The scalar product corresponding to such a norm is numerically realized via the introduction of a (minimal) auxiliary space inspired by the Virtual Element Method. Stability and optimal error estimates in the broken $H^1$ norm are proven under a weak shape regularity assumption allowing the presence of very small edges. The results of numerical tests confirm the theoretical estimates.

翻译：我们建议对多边形熔融的Poisson方程式采用不连续的Galerkin方法,即两个维度的多边形熔融方程式,通过在当地对每个元素的每个元素中涉及通量的剩余术语(以双倍1美元(K)计算)加以处罚而稳定下来。与这种规范相对应的标语产品通过采用虚拟元素法所启发的(最小)辅助空间而从数字上实现。破碎的1美元规范中的稳定性和最佳误差估计,在一种允许存在极小边缘的脆弱常规假设下得到证明。数字测试的结果证实了理论估计。