The Virtual Element Method (VEM) for the elasticity problem is considered in the framework of the Hu-Washizu variational formulation. In particular, a couple of low-order schemes presented in [1], are studied for quadrilateral meshes. The methods under consideration avoid the need of the stabilization term typical of the VEM, due to the introduction of a suitable projection on higher-order polynomials. The schemes are proved to be stable and optimally convergent in a compressible regime, including the case where highly distorted (even non-convex) meshes are employed.

Analysis of a stabilization-free quadrilateral Virtual Element for 2D linear elasticity in the Hu-Washizu formulation / M. Cremonesi, A. Lamperti, C. Lovadina, U. Perego, A. Russo. - In: COMPUTERS & MATHEMATICS WITH APPLICATIONS. - ISSN 0898-1221. - 155:(2024), pp. 142-149. [Epub ahead of print] [10.1016/j.camwa.2023.12.001]

Analysis of a stabilization-free quadrilateral Virtual Element for 2D linear elasticity in the Hu-Washizu formulation

C. Lovadina;
2024

Abstract

The Virtual Element Method (VEM) for the elasticity problem is considered in the framework of the Hu-Washizu variational formulation. In particular, a couple of low-order schemes presented in [1], are studied for quadrilateral meshes. The methods under consideration avoid the need of the stabilization term typical of the VEM, due to the introduction of a suitable projection on higher-order polynomials. The schemes are proved to be stable and optimally convergent in a compressible regime, including the case where highly distorted (even non-convex) meshes are employed.
Convergence and stability analysis; Hu-Washizu formulation; Linear elasticity; Self-stabilized virtual elements; Virtual element method
Settore MAT/08 - Analisi Numerica
2024
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/1022799
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