Conforming/nonconforming virtual elements and application to elasticity problems in curved three-dimensional domains

Abstract The virtual element method (VEM) is a well-established framework for solving partial differential equations on polygonal and polyhedral meshes. In this paper, we introduce a novel hybrid VEM that integrates both conforming and nonconforming virtual spaces. We apply this formulation to a three-dimensional linear elasticity problem, providing rigorous theoretical analysis to demonstrate optimal convergence rates. Furthermore, we extend this approach to domains with curved boundaries, where it naturally provides an exact geometric representation without requiring any structural modifications to the scheme.