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.
| Original language | English (US) |
|---|---|
| Journal | Science China Mathematics |
| Volume | 62 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 1 2019 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
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A unified study of continuous and discontinuous Galerkin methods. / Hong, Qingguo; Wang, Fei; Wu, Shuonan; Xu, Jinchao.
In: Science China Mathematics, Vol. 62, No. 1, 01.01.2019.Research output: Contribution to journal › Review article
TY - JOUR
T1 - A unified study of continuous and discontinuous Galerkin methods
AU - Hong, Qingguo
AU - Wang, Fei
AU - Wu, Shuonan
AU - Xu, Jinchao
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://www.scopus.com/inward/record.url?scp=85056357468&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85056357468&partnerID=8YFLogxK
U2 - 10.1007/s11425-017-9341-1
DO - 10.1007/s11425-017-9341-1
M3 - Review article
AN - SCOPUS:85056357468
VL - 62
JO - Science China Mathematics
JF - Science China Mathematics
SN - 1674-7283
IS - 1
ER -