A Unified Study of Continuous and Discontinuous Galerkin Methods
Abstract
A unified study is presented in this paper for the design and analysis of different finite element methods (FEMs), including conforming and nonconforming FEMs, mixed FEMs, hybrid FEMs,discontinuous Galerkin (DG) methods, hybrid discontinuous Galerkin (HDG) methods and weak Galerkin (WG) methods. Both HDG and WG are shown to admit inf-sup conditions that hold uniformly with respect to both mesh and penalization parameters. In addition, by taking the limit of the stabilization parameters, a WG method is shown to converge to a mixed method whereas an HDG method is shown to converge to a primal method. Furthermore, a special class of DG methods, known as the mixed DG methods, is presented to fill a gap revealed in the unified framework.
Keywords
Cite
@article{arxiv.1712.01211,
title = {A Unified Study of Continuous and Discontinuous Galerkin Methods},
author = {Qingguo Hong and Fei Wang and Shuonan Wu and Jinchao Xu},
journal= {arXiv preprint arXiv:1712.01211},
year = {2018}
}
Comments
39 pages