Accuracy of virtual element with hanging nodes

Abstract

The virtual element method (VEM) is an approximation method for partial differential equations that does not require explicit definition of the interpolation functions for the test and trial functions within the elements. This feature allows VEM to handle elements of arbitrary polygonal or polyhedral shapes, including non-convex ones, without special treatment. Consequently, VEM is attracting attention as a generalization of the finite element method. However, research on VEM has mainly focused on the theoretical aspects, and its application to practical structural analysis has not been sufficiently explored. In this study, we propose to exploit the key advantage of VEM ―its ability to handle arbitrary polygons― in models with hanging nodes, i.e., nodes located on the edges of elements. The analysis of models comprising elements of different sizes connected via hanging nodes indicated that a size ratio of approximately 5 can provide sufficiently accurate results for practical purposes.