Virtual Element Methods Without Extrinsic Stabilization
(2212.01720)Abstract
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 $L2$ projection of the gradient of virtual element functions is computable, and the $L2$ projector has a uniform lower bound on the gradient of virtual element function spaces in $L2$ norm. Optimal error estimates are derived for these VEMs. Numerical experiments are provided to test the VEMs without extrinsic stabilization.
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