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

[摘要] 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. (C) 2016 Elsevier B.V. All rights reserved.

[发布日期] 2016-12-01

[效力级别]  Proceedings Paper

[关键词] HDG;Convergence;Minimal regularity;Postprocessing