A refined a priori error analysis of the lowest-order (linear) nonconforming virtual element method (VEM) for approximating a model Poisson problem is developed in both 2D and 3D. A set of new geometric assumptions is proposed on the shape regularity of polytopal meshes. A new error equation for the lowest-order (linear) nonconforming VEM is derived for any choice of stabilization, and a new stabilization using a projection on an extended element patch is introduced for the error analysis on anisotropic elements.
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Cao et al. (2019) studied this question.
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