Analysis of a stabilization-free quadrilateral Virtual Element for 2D linear elasticity in the Hu-Washizu formulation
COMPUTERS & MATHEMATICS WITH APPLICATIONS(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.
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Key words
Linear elasticity,Hu-Washizu formulation,Virtual element method,Self-stabilized virtual elements,Convergence and stability analysis
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