We analyze the first order Enlarged Enhancement Virtual Element Method (E2VEM) for the Poisson problem. The method allows the definition of bilinear forms that do not require a stabilization term, thanks to the exploitation of higher order polynomial projections that are made computable by suitably enlarging the enhancement property (from which comes the prefix E2) of local virtual spaces. We provide a sufficient condition for the well-posedness and optimal order a priori error estimates. We present numerical tests on convex and non-convex polygonal meshes that confirm the robustness of the method and the theoretical convergence rates.

中文翻译：

---

2D 泊松方程的最低阶自由稳定虚元方法


我们分析了泊松问题的一阶放大增强虚拟元法 （E2VEM）。该方法允许定义不需要稳定项的双线性形式，这要归功于利用高阶多项式投影，这些投影通过适当扩大局部虚拟空间的增强属性（前缀 E2 由此产生）而变得可计算。我们为先验误差估计的适定性和最优阶数提供了充分条件。我们提出了凸面和非凸面多边形网格的数值测试，这些测试证实了该方法的鲁棒性和理论收敛率。