Vem++, a C++ library to handle and play with the virtual element method

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.