On mesh refinement procedures for the virtual element method for two-dimensional elastic problems

Abstract

The virtual element method is an extension of the finite element method permitting arbitrary polygonal/polyhedral element geometry. The method’s mesh flexibility is well-known and is beginning to be exploited in the context of mesh adaptivity. In this work a variety of novel approaches to the computation of isotropic and anisotropic mesh refinement indicators suited to the VEM are presented and comparatively assessed for the case of two-dimensional linear elasticity on structured meshes. Additionally, a novel investigation of the contributions of the two distinctive terms of the VE matrix, the consistency and stabilization terms, in the context of mesh adaptivity is performed. The results demonstrate that the best performance is achieved using combination of refinement procedures based on the displacement and strain fields. Furthermore, the results indicate that the stabilization term can be exploited to enhance adaptive refinement procedures.