Annotations on the virtual element method for second-order elliptic problems

Abstract

This document contains working annotations on the Virtual Element Method (VEM) for the approximate solution of diffusion problems with variable coefficients. To read this document you are assumed to have familiarity with concepts from the numerical discretization of Partial Differential Equations (PDEs) and, in particular, the Finite Element Method (FEM). This document is not an introduction to the FEM, for which many textbooks are available. Eventually, this document will evolve into a tutorial introduction to the VEM (but this is really a long-term goal).