A hybridizable direct discontinuous Galerkin method for elliptic problems

Boundary value problems

Jian Cheng¹  Vladimir Shaydurov¹  Tiegang Liu¹  Huiqiang Yue¹ 

[1] Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, School of Mathematics and Systems Science, Beihang University, Beijing, China

关键词: hybridizable method;    discontinuous Galerkin;    elliptic problem;   

DOI  :  10.1186/s13661-016-0700-x

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The aim of this work is to develop a hybridizable discontinuous Galerkin method for elliptic problems. In the proposed method, the numerical flux functions are constructed from the weak formulation of primal equation directly without converting the second-order equation to a first-order system. In order to guarantee the stability and convergence of the method, we derive a computable lower bound for the constant in numerical flux functions. We also establish a prior error estimation and give some theoretical analysis for the proposed method. Finally, a numerical experiment is presented to verify the theoretical results.

【 授权许可】

CC BY