TY - JOUR
T1 - A unified study of continuous and discontinuous Galerkin methods
AU - Hong, Qingguo
AU - Wang, Fei
AU - Wu, Shuonan
AU - Xu, Jinchao
N1 - Generated from Scopus record by KAUST IRTS on 2023-02-15
PY - 2019/1/1
Y1 - 2019/1/1
N2 - 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.
AB - 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.
UR - http://link.springer.com/10.1007/s11425-017-9341-1
UR - http://www.scopus.com/inward/record.url?scp=85056357468&partnerID=8YFLogxK
U2 - 10.1007/s11425-017-9341-1
DO - 10.1007/s11425-017-9341-1
M3 - Article
SN - 1674-7283
VL - 62
JO - Science China Mathematics
JF - Science China Mathematics
IS - 1
ER -