Improving high-order VEM stability on badly-shaped elements

Stefano Berrone, Gioana Teora and Fabio Vicini

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 216, issue C, 367-385

Abstract: For the 2D and 3D Virtual Element Methods, a new approach to improve the conditioning of local and global matrices in the presence of badly-shaped polytopes is proposed. This new method 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.

Keywords: Ill-conditioning; Virtual element method; Polygonal mesh; Polyhedral mesh; Polynomial basis (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:216:y:2024:i:c:p:367-385

DOI: 10.1016/j.matcom.2023.10.003

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