A priori error analysis of a virtual element approximation-based boundary element method for the electric field integral equation

We develop a Galerkin discretization of the electric field integral equation based on a lowest-order virtual element approximation for surface meshes composed of polygons. This new boundary element discretization relies on the divergence-conforming virtual element counterparts of the classical Raviart- Thomas finite elements on simplices and is particularly suited to handle hanging nodes. We prove the well-posedness of the resulting numerical scheme by establishing the stable-uniform character of the discrete inf-sup condition in the natural norm for polyhedral surfaces. Moreover, we demonstrate through an a priori error analysis the quasi-optimal convergence of the scheme, leading to the same convergence rate as that of the classical Raviart-Thomas boundary element scheme. Finally, numerical experiments involving scattering problems are presented in order to give more insight into the behavior of the virtual boundary element scheme in terms of h-convergence and accuracy as a function of the regularity of solutions and meshes.