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arXiv · 1408.5545

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

Binjie Li·Xiaoping Xie
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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.

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Binjie Li, Xiaoping Xie. 2014-08-24. Analysis of a family of HDG methods for second order elliptic problems. https://arxiv.org/abs/1408.5545

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