A Stabilized Quadratic Virtual Element Formulation With Reduced Degrees of Freedom for Two‐Dimensional Elasticity

ABSTRACT In this work, a stabilized second‐order virtual element method is proposed for two‐dimensional elasticity problems. Relying solely on low‐order degrees of freedom, a Euclidean orthogonal projection in the degree of freedom space is constructed using a least‐squares approach. Leveraging this projection, a streamlined serendipity virtual element scheme is established that eliminates redundant moment degrees of freedom within the standard virtual element, achieving a significant reduction in implementation complexity while preserving high accuracy. To validate the performance of the new element, classical numerical examples are presented, with a special emphasis on bending problems of various beam types solved on an extremely coarse mesh—a demanding capability that is scarcely reported in the existing literature on the virtual element method. The proposed element demonstrates superior accuracy in displacement and stress fields, achieving optimal convergence rates in both the norm and energy semi‐norm. Numerical results indicate that the new element model exhibits remarkable robustness against mesh distortion and inherent geometric adaptability, outperforming existing standard finite element and virtual element models while delivering highly competitive computational accuracy relative to hybrid virtual element models, thereby establishing itself as a reliable and efficient computational tool for continuum solid mechanics.