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

Abstract

In this paper, we analyze a family of hybridizable discontinuous Galerkin (HDG) methods for second order elliptic problems in two and three dimensions. The methods use piecewise polynomials of degree $k⩾0$ for both the flux and numerical trace, and piecewise polynomials of degree $k+1$ for the potential. We establish error estimates for the numerical flux and potential under the minimal regularity condition. Moreover, we construct a local postprocessing for the flux, which produces a numerical flux with better conservation. Numerical experiments in two-space dimensions confirm our theoretical results.

18 pages

References in corpus (2)

• An HDG method for linear elasticity with strong symmetric stresses
• A Weak Galerkin Finite Element Method for the Stokes Equations

Cited by in corpus (1)

• BPX preconditioner for nonstandard finite element methods for diffusion problems