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

TL;DR

This paper provides annotations and insights on the Virtual Element Method (VEM) for solving second-order elliptic diffusion problems with variable coefficients, aiming to deepen understanding and facilitate future tutorials.

Contribution

It offers detailed annotations on VEM for elliptic problems, enhancing comprehension and serving as a foundation for future tutorial development.

Findings

Annotations clarify VEM implementation details

Insights into handling variable coefficients in VEM

Guidance for future tutorial development

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).