Analysis of a family of HDG methods for second order elliptic problems

Binjie Li, Xiaoping Xie

Published 2014-08-24Version 1

In this paper, we propose and analyze a new family of hybridizable discontinuous Galerkin (HDG) methods for second order elliptic problems in two and three dimensions. We use piecewise polynomials of degree $k\geqslant 0$ for both the flux and numerical trace, and piecewise polynomials of degree $k+1$ for the potential. We show the convergence orders of the flux and the potential in $L^2$-norm are $k+1$ and $k+2$, respectively. What's more, we construct a local postprocessing for the flux, which produces a numerical flux with better conservation. We also study the conditioning of the HDG method. We finally do numerical experiments in two-space dimensions to verify our theoretical results.