Interpolation and stability properties of low order face and edge virtual element spaces

TL;DR

This paper investigates the interpolation and stability properties of low order virtual element spaces in 2D and 3D, extending classical polynomial spaces to polygonal meshes and analyzing their application in electromagnetism discretizations.

Contribution

It introduces a detailed analysis of interpolation and stability for virtual element face and edge spaces, generalizing Nédélec and Raviart-Thomas spaces to complex polygonal meshes.

Findings

Interpolation properties are established for virtual element spaces.

Stability of the associated discrete bilinear forms is demonstrated.

Results support the use of virtual elements in electromagnetism simulations.

Abstract

We analyse the interpolation properties of 2D and 3D low order virtual element face and edge spaces, which generalize N\'ed\'elec and Raviart-Thomas polynomials to polygonal-polyhedral meshes. Moreover, we investigate the stability properties of the associated $L^2$ discrete bilinear forms, which typically appear in the virtual element discretization of problems in electromagnetism.