Vem++, a c++ library to handle and play with the Virtual Element Method

Abstract The Virtual Element Method (VEM) is an extension of the Finite Element Method (FEM) to handle polytopal meshes. After giving a short introduction of the VEM for a two dimensional Laplacian problem, we show the differences between an implementation of a VEM and a FEM code highlighting which are the main issues associated with the VEM framework. Furthermore, this paper will show one of the possible ways to face such issues: Vem++ a c++ library developed to “deal and play” with the VEM discretisation. This c++ library deals with the VEM, since there are several partial differential equations in two/three dimensions coming from both academic and engineering problems. Then, one can “play” with the VEM, since Vem++ has been designed so that one can plug-in new features such as new polytopes quadrature rules, new solvers and new virtual element spaces in a smart way.