Improving high order VEM stability on badly-shaped convex elements

02/22/2023

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by   Stefano Berrone, et al.

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For the 2D and 3D Virtual Element Method (VEM), a new approach to improve the conditioning of local and global matrices in presence of badly-shaped polytopes is proposed. It consists in defining 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.