论文标题
虚拟元素方法没有外部稳定
Virtual Element Methods Without Extrinsic Stabilization
论文作者
论文摘要
在任意程度的多项式中没有外部稳定的虚拟元素方法（VEMS）是针对二阶椭圆问题开发的，包括不合格的VEM和任意维度中的符合VEM。关键是要构建本地$ h（\ textrm {div}）$ - 符合宏有限元元素空间，以便可以计算相关的$ l^2 $投影，即虚拟元素函数的梯度投影，并且$ l^2 $投影仪具有统一的lower键在$ l^2 $ norm中的虚拟元素函数梯度上。这些VEM得出了最佳误差估计。提供数值实验以测试VEM，而无需外部稳定。
Virtual element methods (VEMs) without extrinsic stabilization in arbitrary degree of polynomial are developed for second order elliptic problems, including a nonconforming VEM and a conforming VEM in arbitrary dimension. The key is to construct local $H(\textrm{div})$-conforming macro finite element spaces such that the associated $L^2$ projection of the gradient of virtual element functions is computable, and the $L^2$ projector has a uniform lower bound on the gradient of virtual element function spaces in $L^2$ norm. Optimal error estimates are derived for these VEMs. Numerical experiments are provided to test the VEMs without extrinsic stabilization.
