  For the 2D and 3D Virtual Element Methods (VEM), a new approach to improve
the conditioning of local and global matrices in the presence of badly-shaped
polytopes is proposed. It defines the local projectors and the local degrees of
freedom with respect to a set of scaled monomials recomputed on more
well-shaped polytopes. This new approach is less computationally demanding than
using the orthonormal polynomial basis. The effectiveness of our procedure is
tested on different numerical examples characterized by challenging geometries
of increasing complexity.
