Polyhedral mesh quality indicator for the Virtual Element Method

We present the design of a mesh quality indicator that can predict behavior Virtual Element Method (VEM) on given family or finite sequence polyhedral meshes (dataset). The is designed to measure violation regularity assumptions are normally considered in convergence analysis. investigate this new mathematical tool lowest-order conforming approximation three-dimensional Poisson equation. This work also assesses rate VEM when applied very general meshes, including non-convex and skewed elements. Such created within an original generation framework, which allow with different sizes, connectivity, geometrical properties. obtained results show significant correlation between measured priori by effective performance VEM.