Abstract
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.
Highlights
1 Introduction In recent years, the discontinuous Galerkin method (DGM) has been extensively studied by lots of researchers on various problems since it was first introduced by Reed and Hill [ ]
In hybridizable discontinuous Galerkin method (HDGM), additional unknowns defined on interior faces are introduced and the global linear system only involves degrees of freedoms (DOFs) on interior faces
The purpose of this work is to develop a hybridizable discontinuous Galerkin method, which combines the advantages of HDGM and direct discontinuous Galerkin method (DDGM) together, based on the main idea of DDGM
Summary
The discontinuous Galerkin method (DGM) has been extensively studied by lots of researchers on various problems since it was first introduced by Reed and Hill [ ]. In HDGM, additional unknowns defined on interior faces are introduced and the global linear system only involves degrees of freedoms (DOFs) on interior faces. This linear system is smaller than that obtained via classical DGM. One of the key aspects of DDGM is that it directly uses the weak formulation of the original equation instead of rewriting the equations into a first-order system. In this way, the DDGM is easy to implement and more effective because of there being no extra computation for auxiliary variables
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
