From Raviart-Thomas to HDG

TL;DR

This paper introduces the techniques for local analysis of classical mixed methods for diffusion problems and explains how they lead to the development of the Hybridizable Discontinuous Galerkin (HDG) method.

Contribution

It provides an insightful connection between Raviart-Thomas mixed methods and the HDG approach through local analysis techniques.

Findings

Analysis of classical mixed methods for diffusion problems.

Motivation and derivation of the HDG method from existing techniques.

Educational overview of the transition from Raviart-Thomas to HDG.

Abstract

This document has been motivated by a course entitled {\em From Raviart-Thomas to HDG}, prepared for {\em C\'adiz Num\'erica 2013 -- Course and Encounter on Numerical Analysis} (C\'adiz, Spain -- June 2013). It is an introduction to the techniques for local analysis of classical mixed methods for diffusion problems and how they motivate the Hybridizable Discontinuous Galerkin method.