Improving high-order VEM stability on badly-shaped elements

Abstract

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.

References in corpus (2)

• A Hybrid High-Order method for the incompressible Navier--Stokes equations based on Temam's device
• Virtual Element Methods for general second order elliptic problems on polygonal meshes

Cited by in corpus (2)

• The Mixed Virtual Element Discretization for highly-anisotropic problems: the role of the boundary degrees of freedom
• The lowest-order Neural Approximated Virtual Element Method on polygonal elements