We introduce and analyse the first order Enlarged Enhancement Virtual Element Method (E$^2$VEM) 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 (from which comes the prefix of the name E$^2$) property of local virtual spaces. The polynomial degree of local projections is chosen based on the number of vertices of each polygon. We provide a proof of well-posedness and optimal order a priori error estimates. Numerical tests on convex and non-convex polygonal meshes confirm the criterium for well-posedness and the theoretical convergence rates.
翻译:我们引入并分析Poisson问题的第一顺序“扩大增强虚拟元素方法”(E$2$VEM) 。该方法允许对不需要稳定术语的双线形式进行定义,因为利用了较高顺序的多面形预测,这些预测通过适当扩大本地虚拟空间的增强特性(即E$2美元名称的前缀)而进行计算。根据每个多边形的顶点数量选择了多位本地预测度。我们提供了正确储存和最佳顺序的证明,并提供了先验误差估计数。对锥形和非锥形多面形的数值测试证实了精度和理论趋同率的批评。