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

2014/08/24 by Binjie Li, Li, Binjie, Xiaoping Xie +1 · 1 citation
Engineering · Mathematics · #65N12 #65N30 #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1408.5545

openalex publication_date 2014/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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\geqslant 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.

Citations

• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems

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